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(|7x+4|)/(8)=3

$\frac{|7 x+4|}{8}=3$

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Domain and range of absolute value functions: equations

Full solution

Q.

\frac{|7 x+4|}{8}=3

Isolate absolute value: First, let's isolate the absolute value by multiplying both sides by $8$ . $\newline$ $\frac{|7x+4|}{8} \times 8 = 3 \times 8$ $\newline$ $|7x+4| = 24$
Consider two cases: Now we need to consider the two cases for the absolute value. $\newline$ Case $1$ : $7x + 4 = 24$ $\newline$ Case $2$ : $7x + 4 = -24$
Solve Case $1$ : Let's solve Case $1$ . $\newline$ $7x + 4 = 24$ $\newline$ Subtract $4$ from both sides. $\newline$ $7x = 20$ $\newline$ Divide by $7$ . $\newline$ $x = \frac{20}{7}$
Solve Case $2$ : Now, let's solve Case $2$ . $\newline$ $7x + 4 = -24$ $\newline$ Subtract $4$ from both sides. $\newline$ $7x = -28$ $\newline$ Divide by $7$ . $\newline$ $x = -28/7$ $\newline$ $x = -4$

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