Solve the equation for all values of x. |5x-9|+9=x Answer: x=

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Solve the equation for all values of  x.  |5x-9|+9=x Answer:  x=

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Consider Non-Negative Case: We have the equation |5x - 9| + 9 = x. To solve for x, we need to consider two cases because the absolute value function |a| equals a if a is non-negative and -a if a is negative.Simplify Non-Negative Case: First, let's consider the case where the expression inside the absolute value is non-negative, which means 5x - 9 >= 0. In this case, the equation becomes 5x - 9 + 9 = x.Subtract to Solve: Simplify the equation by combining like terms. 5x - 9 + 9 = x 5x = xDivide to Isolate: Subtract x from both sides to solve for x. 5x - x = x - x 4x = 0Consider Negative Case: Divide both sides by 4 to isolate x. 4x / 4 = 0 / 4 x = 0Simplify Negative Case: Now, let's consider the second case where the expression inside the absolute value is negative, which means 5x - 9 < 0. In this case, the equation becomes -(5x - 9) + 9 = x.Add to Solve: Simplify the equation by distributing the negative sign and combining like terms. -(5x - 9) + 9 = x -5x + 9 + 9 = x -5x + 18 = xDivide to Isolate: Add 5x to both sides to solve for x. -5x + 5x + 18 = x + 5x 18 = 6xCheck Solution: Divide both sides by 6 to isolate x. 18 / 6 = 6x / 6 x = 3Substitute x=0: We need to check if our solutions satisfy the original equation. Let's substitute x = 0 into the original equation. |5(0) - 9| + 9 = 0 |-9| + 9 = 0 9 + 9 = 0 This does not hold true, so x = 0 is not a solution.

Solve the equation for all values of $x$ . $\newline$ $|5 x-9|+9=x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|5 x-9|+9=x$ $\newline$ Answer: $x=$