Solve the equation for all values of x. |2x-10|-4=4x Answer: x=

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Solve the equation for all values of  x.  |2x-10|-4=4x Answer:  x=

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Isolate absolute value: We have the equation |2x - 10| - 4 = 4x. To solve for x, we first need to isolate the absolute value expression on one side of the equation. Add 4 to both sides of the equation to isolate the absolute value. |2x - 10| - 4 + 4 = 4x + 4 |2x - 10| = 4x + 4Positive case equation: Now we have |2x - 10| = 4x + 4. The absolute value equation can be split into two separate equations, one for the positive case and one for the negative case. For the positive case: 2x - 10 = 4x + 4Solve positive case: Solve the positive case equation from Step 2. Subtract 2x from both sides: 2x - 10 - 2x = 4x + 4 - 2x -10 = 2x + 4 Now, subtract 4 from both sides: -10 - 4 = 2x + 4 - 4 -14 = 2x Finally, divide by 2: -14 / 2 = 2x / 2 -7 = xNegative case equation: For the negative case, we consider the expression inside the absolute value as negative: -(2x - 10) = 4x + 4 Simplify the negative sign: -2x + 10 = 4x + 4Solve negative case: Solve the negative case equation from Step 4. Add 2x to both sides: -2x + 10 + 2x = 4x + 4 + 2x 10 = 6x + 4 Now, subtract 4 from both sides: 10 - 4 = 6x + 4 - 4 6 = 6x Finally, divide by 6: 6 / 6 = 6x / 6 1 = xCheck x = -7: We have found two potential solutions for x: x = -7 and x = 1. However, we must check these solutions in the original equation to ensure they do not result from extraneous solutions introduced by the absolute value. Check x = -7: |2(-7) - 10| - 4 = 4(-7) |-14 - 10| - 4 = -28 | -24 | - 4 = -28 24 - 4 = -28 20 ≠ -28 The solution x = -7 does not satisfy the original equation, so it is an extraneous solution.Check x = 1: Check x = 1: |2(1) - 10| - 4 = 4(1) |2 - 10| - 4 = 4 |-8| - 4 = 4 8 - 4 = 4 4 = 4 The solution x = 1 satisfies the original equation, so it is a valid solution.

Solve the equation for all values of $x$ . $\newline$ $|2 x-10|-4=4 x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|2 x-10|-4=4 x$ $\newline$ Answer: $x=$