Solve the equation for all values of x. |3x-5|=2x Answer: x=

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Solve the equation for all values of  x.  |3x-5|=2x Answer:  x=

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Split Absolute Value: We have the equation |3x - 5| = 2x. The absolute value equation can be split into two separate equations, one for the positive case and one for the negative case. For the positive case, we simply remove the absolute value bars: 3x - 5 = 2xPositive Case Solution: Now, let's solve the equation 3x - 5 = 2x. Subtract 2x from both sides to isolate x on one side: 3x - 2x - 5 = 2x - 2x x - 5 = 0Positive Case Equation Solving: Add 5 to both sides to solve for x: x - 5 + 5 = 0 + 5 x = 5 This is the solution for the positive case.Positive Case Final Solution: For the negative case, we consider the expression inside the absolute value to be negative: -(3x - 5) = 2x This simplifies to: -3x + 5 = 2xNegative Case Consideration: Now, let's solve the equation -3x + 5 = 2x. Add 3x to both sides to get all the x terms on one side: -3x + 3x + 5 = 2x + 3x 5 = 5xNegative Case Equation Solving: Divide both sides by 5 to solve for x: 5/5 = 5x/5 1 = x This is the solution for the negative case.Negative Case Final Solution: We need to check if our solutions satisfy the original equation |3x - 5| = 2x. Let's first check x = 5: |3(5) - 5| = 2(5) |15 - 5| = 10 |10| = 10 Since 10 is positive, the absolute value of 10 is indeed 10. So, x = 5 is a valid solution.Solution Checking for x = 5: Now, let's check x = 1: |3(1) - 5| = 2(1) |3 - 5| = 2 |-2| = 2 Since the absolute value of -2 is 2, x = 1 is also a valid solution.

Solve the equation for all values of $x$ . $\newline$ $|3 x-5|=2 x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|3 x-5|=2 x$ $\newline$ Answer: $x=$