Solve for all values of x in simplest form. 2+3|4x+2|=38 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 + 3|4x + 2| - 2 = 38 - 2 3|4x + 2| = 36Divide by 3: Divide both sides of the equation by 3 to solve for the absolute value expression. 3|4x + 2| / 3 = 36 / 3 |4x + 2| = 12Set 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: 4x + 2 = 12 Case 2: 4x + 2 = -12Solve for x in Case 1: Solve for x in Case 1. Subtract 2 from both sides of the equation: 4x + 2 - 2 = 12 - 2 4x = 10 Divide both sides by 4: 4x / 4 = 10 / 4 x = 10 / 4 x = 2.5Solve for x in Case 2: Solve for x in Case 2. Subtract 2 from both sides of the equation: 4x + 2 - 2 = -12 - 2 4x = -14 Divide both sides by 4: 4x / 4 = -14 / 4 x = -14 / 4 x = -3.5

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Solve for all values of
x in simplest form.

2+3|4x+2|=38
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $2+3|4 x+2|=38$ $\newline$ 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+3|4 x+2|=38

\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: $\newline$ $2 + 3|4x + 2| - 2 = 38 - 2$ $\newline$ $3|4x + 2| = 36$
Divide by $3$ : Divide both sides of the equation by $3$ to solve for the absolute value expression. $\newline$ $\frac{3|4x + 2|}{3} = \frac{36}{3}$ $\newline$ $|4x + 2| = 12$
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 $1$ : $4x + 2 = 12$ $\newline$ Case $2$ : $4x + 2 = -12$
Solve for x in Case $1$ : Solve for x in Case $1$ . $\newline$ Subtract $2$ from both sides of the equation: $\newline$ $4x + 2 - 2 = 12 - 2$ $\newline$ $4x = 10$ $\newline$ Divide both sides by $4$ : $\newline$ $\frac{4x}{4} = \frac{10}{4}$ $\newline$ $x = \frac{10}{4}$ $\newline$ $x = 2.5$
Solve for x in Case $2$ : Solve for x in Case $2$ . $\newline$ Subtract $2$ from both sides of the equation: $\newline$ $4x + 2 - 2 = -12 - 2$ $\newline$ $4x = -14$ $\newline$ Divide both sides by $4$ : $\newline$ $\frac{4x}{4} = \frac{-14}{4}$ $\newline$ $x = \frac{-14}{4}$ $\newline$ $x = -3.5$