Which Equation Has Only One Solution. Upon evaluating all four equations, Equation D is the only one that

Upon evaluating all four equations, Equation D is the only one that results in exactly one solution. When the absolute value expression is on one side of the equation and the constant of 0 0 0 on the other, then we know that there is only one solution when the value within the signs of the … The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and … Learn how to tell if a system of equations has one, no, or infinite solutions. Equation: The absolute value of a number is zero … If the determinant is non-zero, the matrix is invertible, and the system has exactly one solution. Based on this analysis: Equation 1 has no solutions. In this case, the equation that meets this … Notice that for any value of x x x, the absolute value on the right side is a positive result. An example of an equation with no solutions is ∣x∣ = −3, as … An equation that has only one solution is generally referred to as a linear equation. Therefore, option D is the only equation where the absolute … Upload your school material for a more relevant answer The linear equation which has only one solution would be |–6x + 3| = 0 What is a linear equation? A linear equation is an … A linear system Ax=b has one of three possible solutions:1. The system has a unique solution which means only one solution. Which equation has only one solution? The | - 6x + 3| = 0 has only one solution for x which satisfies the value of x = 1/ 2. This SAT Math guide explains patterns and strategies to … In this video I explain how to determine if a system of linear equations has no solution, one solution or infinitely many solutions, including several exampl Introduction There are three cases that can come up as we are solving linear equations. ∣ −6x +3∣ = 0 because an absolute value is zero only when its argument is zero, resulting in exactly one solution. Therefore, the equation In general, a linear equation in one variable has only one solution. Visually, this means the graph … To determine which of the given equations has only one solution, we need to analyze each equation using the concept of the discriminant in quadratic equations. The system has no solution. Solutions represent the values of unknown variables; the more the solutions, the more the values of the unknown variable. After analyzing each equation, we find that the equation ∣ − 6x + 3∣ = 0 is the only one with exactly one solution. Solve for x: −6x = −3 x … Equation: ∣ −6x +3∣ = 0 The absolute value of an expression is zero only when the expression itself is zero. From the above examples, we see that the variable x does not disappear after solving & we say that the linear equation will … You have seen that if an equation has no solution, you end up with a false statement instead of a value for x. e. This is consistent across all absolute value equations. An equation has only one solution if it can be expressed in the form of a perfect square trinomial, … A linear equation is a type of equation in which the degree of each variable in the equation is exactly equal to one. The absolute value function is defined such that it always yields non-negative results, which means any absolute value equation equated to a negative number will have no … The equation that has only one solution is Option B: 4m + 5 = 25, which simplifies to m = 5. For this absolute value equation, ∣ − 6x + 3∣ = 0, the only way for an absolute value to be zero is if the expression inside the absolute value is zero itself. Thus, the fourth equation has only one solution: x = 21 . After examining each equation, only Equation 4, ∣ − 6x + 3∣ = 0, has exactly one solution, which is x = 0. This helps reinforce the understanding that absolute values equaling zero … The properties of absolute value dictate that absolute values are always non-negative, and that they equal zero only when the inner expression is zero, confirming that … The analysis of absolute value equations shows that they have specific criteria for having one or more solutions. Consider equation x 2 + x Taking the common factor out, ⇒ x (x + 1) = 0 Using … I tried to find the value of $m$, for which $x$ has only one solution. Here is my proof but I am not sure whether it's correct or not. This equation has only one solution, x = 21 . What is the sum of those values of ? Solution 1 A quadratic equation has exactly distinct root if and only if … It is not obvious, at this stage, whether the system of linear equations has a unique solution, has infinitely many solutions, or does not … Not only the typical inference questions but also all other CR questions on the GMAT require the ability to deduce from the given information. I'm more used to the formulation in the following form: $$ X (2^ {P+Q} - 3^P)=2^Q-1 \\ 2^Q (2^Px -1) = 3^Px -1 $$ and then $$ 2^Q = {3^P \cdot X - 1 \over 2^P \cdot X - 1} \tag 1 … Carly, sandi, cyrus and pedro have multiple pets. Solving for x gives a single solution. This algebra video tutorial explains how to determine if a system of equations contain one solution, no solution, or infinitely many solutions. We know this because the absolute value of a number equals zero, only when that number itself is zero. The equation that has only one solution is ∣ − 6x + 3∣ = 0. This is because it is the only equation where the absolute value is equal to zero, yielding a single solution for x. Conclusion Comparing the number of solutions for each equation, we find that only equation 4, ∣ − 6x + 3∣ = 0, has exactly one … The properties of absolute values dictate that ∣A∣ = 0 yields only one solution, specifically A = 0. Again, there is exactly one solution. com | In this lesson, I'll show you how you can see from its graph whether a quadratic equation only has one solution (root)! The equation that has only one solution is option D: ∣ − 6x + 3∣ = 0, which results in the solution x = 0. I solved it by calculating the discriminant: $\sqrt { (-m)^2-4ma+4a^2}=0$ which gives $m=2a$ I tried to find the value of $m$, for which $x$ has only one solution. In this item, our goal is to determine which of the given absolute equations has only one solution. A common form of a linear equation is ax + b = c, where a, b, and c are constants and a is not equal to zero. STEADFASTtutoring. A linear equation is a type of equation in which the degree of each variable in the equation is exactly … This algebra video tutorial explains how to determine if a system of equations contain one solution, no solution, or infinitely many solutions. sandi and pedro have chickens. The other options either have infinite solutions or no solutions at all. The equation that has only one solution is Equation D: ∣ −6x +3∣ = 0, which yields the solution x = 21. But, when we … Based on mathematical principles, the absolute value cannot equal a negative number, explaining why option A has no solution. How to prove the equations have only one real solution? Ask Question Asked 2 years, 2 months ago Modified 2 years, 2 months ago Which equation has only one solution? - 16293402Answer: options d has only one solution because zero neither be positive nor be … For example, if you take ∣ −6x +3∣ = 0, the only number that satisfies this equation is when the inside expression equals zero, leading to a unique solution. An equation with only one solution can be a linear equation such as 2x +4 = 0 or a quadratic equation with a zero discriminant like x2 … The properties of absolute values state that they cannot be negative, proving that no solutions exist for ∣x − 5∣ = −1, and that equality to zero yields a unique solution. The equation that has only one solution is ∣ − 6x + 3∣ = 0, which uniquely gives x = 21. [tex]\ (|-6-2x|=8\) [/t… - brainly. This is because the value inside the absolute function can only equal zero, giving one unique solution. Divide by -6: x = 21 = 0. Options B and D have infinite solutions, while option C has no solution. everyone except carly has a rabbit. It is possible to have an equation where any value for x will provide a solution to … A one-solution equation (also called a linear equation) is an equation with only one variable, and the highest degree of the variable is 1. An absolute value equation has one solution when set equal to … . In a system, each equation represents one condition, and the solution is the pair (or set) of values that satisfies all conditions at the same time. www. How Do you Tell if an Equation has One Solution, No solution, or Infinite Solutions? When you are working with systems of linear equations there … The equation that has only one solution is D: |–6x + 3| = 0. Let us … For instance, the equation |x-5|=3 has two solutions, x=8 and x=2, confirming that absolute value equations can often have more than one solution depending on how they are … A quadratic equation has one solution when the discriminant is zero. An example of an absolute value equation with two solutions is ∣x + 2∣ = 4, which gives solutions x = 2 and x = −6. These equations have only one solution. Solving for x, we get −6x = −3, so x = −6−3 = 21 . Come master how to draw … To determine which equation has only one distinct solution, we need to analyze each quadratic equation given: Quadratic equations can have one, two, or no real solutions. [tex]\ (|x-5|=-1\) [/tex] B. In general terms, … Click here 👆 to get an answer to your question ️ Which equation has only one solution? |x-5|=-1 |-6-2x|+8 |5x+10|=10 beginvmatrix -6x+3endvmatrix =0 One Solution Equation is when an equation has only one solution. I am aware of the existence of discriminants and their role of solving system of linear equations, although I have no idea on … Under what conditions on a and b will the following linear system have no solutions, one solution, infinitely many solutions? first row: 2x − 3y = a second row: 4x − 6y = b My work: … For example, the equation y = ∣x∣ equals 0 only at x = 0, demonstrating that absolute value equations can often yield unique solutions when set to zero. In most cases, this means finding a specific value …. All four equations have a unique solution, but if we need to … Therefore, this equation has no solution. Therefore, we set: −6x + 3 = 0. … −6x + 3 = 0. While a quadratic equation, written as $ax^2 + bx + c = … To determine which equation has only one solution, we need to examine the given options. Therefore, this equation has one solution. In mathematics, an absolute value equation can produce a single solution only when it equals zero, as explained in the analysis of the fourth equation. We have to find the nature of the solution. The other equations either have no solution or two solutions. … Use this list of examples of one solution equations, zero solution equations, and infinite solutions equations to master this topic! Hence, the given linear equation has only one solution i. x = 80. Therefore, the correct answer is D: ∣− 6x + 3∣ = 0 with the solution being x = 0. To determine which system of equations has only one solution, we need to analyze each of the given systems. Equation 3 typically has two solutions. Conclusion Therefore, the equation with only one solution is ∣ − 6x + 3∣ … Click here 👆 to get an answer to your question ️ Which equation has only one solution? |x-5|=-1 |-6-2x|=8 |5x+10|=10 |-8x+3|=0 This answer is FREE! See the answer to your question: Which equation has only one solution? A. carly and sandi have dogs, while the other two have cats. An equation has only one solution if it can be expressed in the form of a perfect square trinomial, … Which of the following equations has only one solution? x2 = 9, x(x - 1) = 9, x2 - 6x + 9 = 0 - The equation x2 - 6x + 9 = 0 has only one solution x = 3. The equation that has only one solution is D. All other equations produce two solutions or no solutions. 3. 2. Solution: To find which equation has only one solution, we will solve for x in each of the given equations. 5. Subtract 3 from both sides: −6x = −3. An equation that has only one solution is generally referred to as a linear equation. This gives us: −6x + 3 = 0 Solving for x: −6x = −3 x = 0. For example, the absolute value equation ∣x∣ = c has only one solution when c = 0. Other equations either have no solutions or two solutions. The properties of absolute values dictate that an absolute value equation will have one solution if the expression inside the absolute value equals zero, leading to a single … Consider similar equations such as ∣x +2∣ = 3, which has two solutions, or ∣x − 1∣ = 0, which has one solution. The equation that has only one solution is the one where the absolute value of the expression inside it is equal to a specific number. com The equation that has only one solution is ∣ − 6x + 3∣ = 0, which gives the solution x = 21. The … The equation with only one solution is option A: 2a+ 7 = a+ 10 which simplifies to a = 3. The concept of a unique solution applies to equations where the variable has an exponent greater than one, such as quadratic equations. 5 This … When we solve a linear equation in one variable, we may find exactly one value of x that will make the equation a true statement. … Sure! Let's analyze each equation step by step to determine which one has only one solution: Equation: ∣x − 5∣ = −1 The absolute value of any expression is always non-negative, … The absolute value equation ∣ − 6x + 3∣ = 0 implies that the expression inside the absolute value must be zero since absolute values cannot be negative: −6x + 3 = 0 Solving … For the equation ∣ − 6x + 3∣ = 0, the absolute value of an expression equals 0 only when the expression inside is exactly 0. To determine which equation has only one solution, we will examine each equation individually and evaluate the nature of their solutions based on absolute values. For example, the equation ∣x − 2∣ = 3 has two solutions: x = 5 and x = −1 while ∣ − 7+ 2x∣ = 0 has only one solution when the expression inside the absolute value equals zero. Linear equations in one variable are those equations in which there is … I want to prove that the equation $ e^ {-x} = x $ has only one solution in $ \left (0, 1\right) $. This means that when you solve an equation, the variable can only be subsituted by ONE number to make an equation true. The other equations either have two solutions or no solution at all. For any positive value of c, it has two solutions: one positive and one negative. From an algebra standpoint, this means b2 = 4ac. Carly, sandi, cyrus and pedro have multiple pets. We have already seen one, where an equation has one solution. Step 3: Graphical Interpretation: Plot the … An example illustrating why Equation D has only one solution is that the absolute value is zero only when the content inside is precisely zero, as shown in the steps of solving it. 4. The equation that has only one solution is given by D) |-6x+3| = 0. In contrast, equations like y = ∣x … If there exists more than one real solution for $f (x)=0$ then $f (a)=0=f (b)\implies a=b$, and thus there is only one real solution to the equation, … Problem There are two values of for which the equation has only one solution for . Equation 2 typically has two solutions. Equation: ∣ −6 − 2x∣ = 8 An equation of the form ∣a∣ = b where b> 0 typically has two solutions, as the expression inside the absolute … To determine which equation has only one solution, let's analyze each option step-by-step: The absolute value of any expression is always non-negative (0 or positive). On the left side, there is a negative value. A system of linear equations has one solution if the lines represented by the … Two lines a 1 + b 1 y + c 1 = 0 and a 2 x + b 0 y + c 2 = 0, if the denominator a 1 b 2 – a 2 b 1 ≠ 0 then the given system of equations has unique … Equation: Similarly, we will consider two cases: - First Case: - Second Case: This equation also has two solutions: and . Sometimes we come across equations … To determine which equation has only one solution, we need to examine the given options. To do this, we need to recall how to find the solution to an absolute value function. The first equation has no solution, while the second and third have two solutions each. I solved it by calculating the discriminant: $\sqrt { (-m)^2-4ma+4a^2}=0$ which gives $m=2a$ And the assignment to prove that it has only one solution. Given, a linear equation in one variable. ct0ollb
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