Solve the equation for all values of x. |4x+2|-8=x Answer: x=

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Solve the equation for all values of  x.  |4x+2|-8=x Answer:  x=

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Isolate absolute value: We have the equation |4x+2|-8=x. To solve for x, we first need to isolate the absolute value expression on one side of the equation. Add 8 to both sides of the equation to isolate the absolute value. |4x+2|-8+8=x+8 |4x+2|=x+8Split into two equations: Now we have |4x+2|=x+8. The absolute value equation can be split into two separate equations because the expression inside the absolute value can be either positive or negative. The two cases are: 1. 4x+2 = x+8 (when the expression inside the absolute value is positive or zero) 2. 4x+2 = -(x+8) (when the expression inside the absolute value is negative)Solve first case: Solve the first case 4x+2 = x+8. Subtract x from both sides: 4x - x + 2 = x - x + 8 3x + 2 = 8 Subtract 2 from both sides: 3x + 2 - 2 = 8 - 2 3x = 6 Divide both sides by 3: 3x/3 = 6/3 x = 2Solve second case: Solve the second case 4x+2 = -(x+8). Distribute the negative sign on the right side: 4x + 2 = -x - 8 Add x to both sides: 4x + x + 2 = -x + x - 8 5x + 2 = -8 Subtract 2 from both sides: 5x + 2 - 2 = -8 - 2 5x = -10 Divide both sides by 5: 5x/5 = -10/5 x = -2Check solutions: We have found two potential solutions for the equation |4x+2|-8=x: x = 2 and x = -2. However, we must check these solutions in the original equation to ensure they do not create any contradictions, as sometimes absolute value equations can yield extraneous solutions. Check x = 2: |4(2)+2|-8=2 |8+2|-8=2 |10|-8=2 10-8=2 2=2 (This is true, so x = 2 is a valid solution.) Check x = -2: |4(-2)+2|-8=-2 |-8+2|-8=-2 |-6|-8=-2 6-8=-2 -2=-2 (This is true, so x = -2 is also a valid solution.)

Solve the equation for all values of $x$ . $\newline$ $|4 x+2|-8=x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|4 x+2|-8=x$ $\newline$ Answer: $x=$