Solve the equation for all values of x. |3x-4|=x Answer: x=

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Solve the equation for all values of  x.  |3x-4|=x Answer:  x=

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Absolute Value Equation: We have the equation |3x - 4| = x. To solve this, we need to consider two cases because the absolute value function outputs the distance from zero, which can be either positive or negative. Case 1: When the expression inside the absolute value is non-negative, we can remove the absolute value bars without changing the sign. Case 2: When the expression inside the absolute value is negative, we remove the absolute value bars and change the sign of the expression inside.Case 1 Solution: Solve for Case 1 where the expression inside the absolute value is non-negative. 3x - 4 = x Subtract x from both sides to get the x terms on one side. 3x - x - 4 = x - x 2x - 4 = 0 Add 4 to both sides to isolate the term with x. 2x - 4 + 4 = 0 + 4 2x = 4 Divide both sides by 2 to solve for x. 2x / 2 = 4 / 2 x = 2Case 2 Solution: Solve for Case 2 where the expression inside the absolute value is negative. -(3x - 4) = x Distribute the negative sign inside the parentheses. -3x + 4 = x Add 3x to both sides to get the x terms on one side. -3x + 3x + 4 = x + 3x 4 = 4x Divide both sides by 4 to solve for x. 4 / 4 = 4x / 4 1 = xCheck Solutions: Check the solutions in the original equation to ensure they do not result in a negative inside the absolute value when it should be positive or vice versa. For x = 2: |3(2) - 4| = 2 |6 - 4| = 2 |2| = 2 2 = 2 which is true.  For x = 1: |3(1) - 4| = 1 |3 - 4| = 1 |-1| = 1 1 = 1 which is true.  Both solutions satisfy the original equation.

Solve the equation for all values of $x$ . $\newline$ $|3 x-4|=x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|3 x-4|=x$ $\newline$ Answer: $x=$