Solve the equation for all values of x. |4x+7|=3x Answer: x=

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Solve the equation for all values of  x.  |4x+7|=3x Answer:  x=

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Understand absolute value equation: Understand the absolute value equation |4x+7|=3x. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, |4x+7| can be either 4x+7 or -(4x+7) depending on the value of x.Set up two equations: Set up two separate equations to solve for x, one for each case of the absolute value. Case 1: 4x + 7 = 3x Case 2: -(4x + 7) = 3xSolve first case: Solve the first case 4x + 7 = 3x. Subtract 3x from both sides to isolate x. 4x + 7 - 3x = 3x - 3x x + 7 = 0 Subtract 7 from both sides to solve for x. x = -7Solve second case: Solve the second case -(4x + 7) = 3x. First, distribute the negative sign inside the parentheses. -4x - 7 = 3x Add 4x to both sides to get all x terms on one side. -4x - 7 + 4x = 3x + 4x -7 = 7x Divide both sides by 7 to solve for x. x = -7 / 7 x = -1Check first solution: Check both solutions in the original equation to ensure they are valid. For x = -7: |4(-7) + 7| = 3(-7) |-28 + 7| = -21 |-21| = -21 21 ≠ -21, so x = -7 is not a solution.Check second solution: Check the second solution x = -1 in the original equation. |4(-1) + 7| = 3(-1) |-4 + 7| = -3 |3| = -3 3 ≠ -3, so x = -1 is not a solution either.Conclude no solutions: Since neither of the found values for x satisfy the original equation, we conclude that there are no solutions to the equation |4x+7|=3x.

Solve the equation for all values of $x$ . $\newline$ $|4 x+7|=3 x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|4 x+7|=3 x$ $\newline$ Answer: $x=$