Solve the equation for all values of x. |2x+1|-8=x Answer: x=

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Solve the equation for all values of  x.  |2x+1|-8=x Answer:  x=

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Consider Non-Negative Case: We have the equation |2x+1|-8=x. To solve for x, we need to consider two cases because of the absolute value: one where 2x+1 is non-negative and one where 2x+1 is negative.Simplify Non-Negative Case: First, let's consider the case where 2x+1 is non-negative. In this case, the absolute value expression |2x+1| is just 2x+1. So the equation becomes: 2x+1-8=xIsolate Variable (Non-Negative): Simplify the equation by subtracting 1 and adding 8 to both sides: 2x+1-8=x 2x-7=xAdd 7 (Non-Negative): Now, subtract x from both sides to isolate the variable: 2x-7-x=x-x x-7=0Consider Negative Case: Add 7 to both sides to solve for x: x-7+7=0+7 x=7 This is the solution for the case where 2x+1 is non-negative.Distribute Negative Sign: Now, let's consider the case where 2x+1 is negative. In this case, the absolute value expression |2x+1| is -(2x+1). So the equation becomes: -(2x+1)-8=xCombine Like Terms: Distribute the negative sign inside the parentheses: -2x-1-8=xIsolate Variable (Negative): Combine like terms by adding 1 and 8 to both sides: -2x-1-8+1+8=x+1+8 -2x=x+9Subtract 9: Add 2x to both sides to isolate the variable: -2x+2x=x+9+2x 0=3x+9Divide by 3: Subtract 9 from both sides to solve for x: 0-9=3x+9-9 -9=3xDivide both sides by 3 to find the value of x: -9/3=3x/3 -3=x This is the solution for the case where 2x+1 is negative.

Solve the equation for all values of $x$ . $\newline$ $|2 x+1|-8=x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|2 x+1|-8=x$ $\newline$ Answer: $x=$