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

Write Equation: Write down the given equation. |4x - 4| - 4 = 2x We need to solve for x.Isolate Absolute Value: Isolate the absolute value expression on one side of the equation. Add 4 to both sides of the equation to isolate the absolute value. |4x - 4| - 4 + 4 = 2x + 4 |4x - 4| = 2x + 4Set Up Equations: Set up two separate equations to account for the absolute value. Since |A| = B implies A = B or A = -B, we have: 4x - 4 = 2x + 4 or 4x - 4 = -(2x + 4)Solve First Equation: Solve the first equation 4x - 4 = 2x + 4. Subtract 2x from both sides: 4x - 4 - 2x = 2x + 4 - 2x 2x - 4 = 4 Add 4 to both sides: 2x - 4 + 4 = 4 + 4 2x = 8 Divide by 2: x = 8 / 2 x = 4Solve Second Equation: Solve the second equation 4x - 4 = -(2x + 4). Distribute the negative sign on the right side: 4x - 4 = -2x - 4 Add 2x to both sides: 4x - 4 + 2x = -2x - 4 + 2x 6x - 4 = -4 Add 4 to both sides: 6x - 4 + 4 = -4 + 4 6x = 0 Divide by 6: x = 0 / 6 x = 0

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Solve the equation for all values of
x.

|4x-4|-4=2x
Answer:
x=

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

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Math Problems

Grade 8

Evaluate absolute value expressions

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Q. Solve the equation for all values of

x

\newline

|4 x-4|-4=2 x

\newline

Answer:

x=

Write Equation: Write down the given equation. $\newline$ $\lvert 4x - 4 \rvert - 4 = 2x$ $\newline$ We need to solve for $x$ .
Isolate Absolute Value: Isolate the absolute value expression on one side of the equation. $\newline$ Add $4$ to both sides of the equation to isolate the absolute value. $\newline$ $|4x - 4| - 4 + 4 = 2x + 4$ $\newline$ $|4x - 4| = 2x + 4$
Set Up Equations: Set up two separate equations to account for the absolute value. $\newline$ Since $|A| = B$ implies $A = B$ or $A = -B$ , we have: $\newline$ $4x - 4 = 2x + 4$ or $4x - 4 = -(2x + 4)$
Solve First Equation: Solve the first equation $4x - 4 = 2x + 4$ . $\newline$ Subtract $2x$ from both sides: $\newline$ $4x - 4 - 2x = 2x + 4 - 2x$ $\newline$ $2x - 4 = 4$ $\newline$ Add $4$ to both sides: $\newline$ $2x - 4 + 4 = 4 + 4$ $\newline$ $2x = 8$ $\newline$ Divide by $2$ : $\newline$ $x = \frac{8}{2}$ $\newline$ $x = 4$
Solve Second Equation: Solve the second equation $4x - 4 = -(2x + 4)$ . $\newline$ Distribute the negative sign on the right side: $\newline$ $4x - 4 = -2x - 4$ $\newline$ Add $2x$ to both sides: $\newline$ $4x - 4 + 2x = -2x - 4 + 2x$ $\newline$ $6x - 4 = -4$ $\newline$ Add $4$ to both sides: $\newline$ $6x - 4 + 4 = -4 + 4$ $\newline$ $6x = 0$ $\newline$ Divide by $6$ : $\newline$ $x = 0 / 6$ $\newline$ $4x - 4 = -2x - 4$ $0$