Solve for all values of x in simplest form. 2+2|2x-3|=22 Answer: x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. Subtract 2 from both sides of the equation to get: 2 + 2|2x - 3| - 2 = 22 - 2 Simplify both sides: 2|2x - 3| = 20Divide by 2: Divide both sides of the equation by 2 to solve for the absolute value expression. 2|2x - 3| / 2 = 20 / 2 Simplify both sides: |2x - 3| = 10Set up two equations: Set up two separate equations to account for the two possible cases of the absolute value (one where the expression inside is positive and one where it is negative). Case 1: 2x - 3 = 10 Case 2: 2x - 3 = -10Solve for x in Case 1: Solve for x in Case 1. Add 3 to both sides of the equation: 2x - 3 + 3 = 10 + 3 Simplify: 2x = 13 Divide both sides by 2: x = 13 / 2 x = 6.5Solve for x in Case 2: Solve for x in Case 2. Add 3 to both sides of the equation: 2x - 3 + 3 = -10 + 3 Simplify: 2x = -7 Divide both sides by 2: x = -7 / 2 x = -3.5

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Solve for all values of
x in simplest form.

2+2|2x-3|=22
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $2+2|2 x-3|=22$ $\newline$ Answer: $x=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

2+2|2 x-3|=22

\newline

Answer:

x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. $\newline$ Subtract $2$ from both sides of the equation to get: $\newline$ $2 + 2|2x - 3| - 2 = 22 - 2$ $\newline$ Simplify both sides: $\newline$ $2|2x - 3| = 20$
Divide by $2$ : Divide both sides of the equation by $2$ to solve for the absolute value expression. $\newline$ $\frac{2|2x - 3|}{2} = \frac{20}{2}$ $\newline$ Simplify both sides: $\newline$ $|2x - 3| = 10$
Set up two equations: Set up two separate equations to account for the two possible cases of the absolute value (one where the expression inside is positive and one where it is negative). $\newline$ Case $1$ : $2x - 3 = 10$ $\newline$ Case $2$ : $2x - 3 = -10$
Solve for x in Case $1$ : Solve for x in Case $1$ . $\newline$ Add $3$ to both sides of the equation: $\newline$ $2x - 3 + 3 = 10 + 3$ $\newline$ Simplify: $\newline$ $2x = 13$ $\newline$ Divide both sides by $2$ : $\newline$ $x = \frac{13}{2}$ $\newline$ $x = 6.5$
Solve for x in Case $2$ : Solve for x in Case $2$ . $\newline$ Add $3$ to both sides of the equation: $\newline$ $2x - 3 + 3 = -10 + 3$ $\newline$ Simplify: $\newline$ $2x = -7$ $\newline$ Divide both sides by $2$ : $\newline$ $x = \frac{-7}{2}$ $\newline$ $x = -3.5$