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-8|3x+2|+9=-55

$-8|3 x+2|+9=-55$

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Integer inequalities with absolute values

Full solution

Q.

-8|3 x+2|+9=-55

Isolate absolute value: First, let's isolate the absolute value by moving the $9$ to the other side of the equation. $\newline$ $-8|3x+2| = -55 - 9$ $\newline$ $-8|3x+2| = -64$
Divide by $-8$ : Now, divide both sides by $-8$ to get the absolute value by itself. $\newline$ $|3x+2| = -64 / -8$ $\newline$ $|3x+2| = 8$
Set up equations: Next, we set up two equations to solve for the values inside the absolute value, because if $|A| = B$ , then $A = B$ or $A = -B$ . So we have: $3x + 2 = 8$ and $3x + 2 = -8$
Solve first equation: Let's solve the first equation: $\newline$ $3x + 2 = 8$ $\newline$ $3x = 8 - 2$ $\newline$ $3x = 6$ $\newline$ $x = \frac{6}{3}$ $\newline$ $x = 2$
Solve second equation: Now, let's solve the second equation: $\newline$ $3x + 2 = -8$ $\newline$ $3x = -8 - 2$ $\newline$ $3x = -10$ $\newline$ $x = \frac{-10}{3}$ $\newline$ $x = -\frac{10}{3}$ or $-3.33\ldots$

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