Solve the equation for all values of x. |2x-1|+5=4x Answer: x=

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Solve the equation for all values of  x.  |2x-1|+5=4x Answer:  x=

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Consider Non-Negative Case: We have the equation |2x-1| + 5 = 4x. 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 Equation: First, let's consider the case where 2x - 1 is non-negative, which means 2x - 1 >= 0. In this case, the absolute value expression |2x - 1| is just 2x - 1. So the equation becomes: 2x - 1 + 5 = 4xIsolate x: Simplify the equation by combining like terms: 2x + 4 = 4xCheck Validity for x=2: To isolate x, we subtract 2x from both sides of the equation: 4 = 2xConsider Negative Case: Divide both sides by 2 to solve for x: x = 2Distribute Negative Sign: Now, let's consider the second case where 2x - 1 is negative, which means 2x - 1 < 0. In this case, the absolute value expression |2x - 1| is -(2x - 1). So the equation becomes: -(2x - 1) + 5 = 4xCombine Like Terms: Distribute the negative sign inside the parentheses: -2x + 1 + 5 = 4xDivide by 6: Combine like terms: 6 = 6xCheck Validity for x=1: Divide both sides by 6 to solve for x: x = 1We need to check if our solutions satisfy the original equation. For x = 2, the original equation |2x-1|+5=4x becomes |4-1|+5=8, which simplifies to 3+5=8. This is true, so x = 2 is a valid solution.For x = 1, the original equation |2x-1|+5=4x becomes |2-1|+5=4, which simplifies to 1+5=4. This is not true, so x = 1 is not a valid solution.

Solve the equation for all values of $x$ . $\newline$ $|2 x-1|+5=4 x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|2 x-1|+5=4 x$ $\newline$ Answer: $x=$