Question

Solve the following equation.

LaTeX: \left|\frac{x}{7}\right|=1| x 7 | = 1

Group of answer choices

LaTeX: x=7 x = 7

LaTeX: x=-4,\:x=-16 x = − 4 , x = − 16

LaTeX: x=7,\:x=-7 x = 7 , x = − 7

LaTeX: x=-5,\:x=-13

Answer 1

Answer:

x = +7, x = -7

Explanation:

The equation to solve is:

$\left|\frac{x}{7}\right|=1$

Which means that the absolute value of the fraction $\frac{x}{7}$ must be equal to 1. Since we have an absolute value, we have basically two equations to solve:

1) $\frac{x}{7}=+1$

Solving this one, we find

$\frac{x}{7}\cdot 7 = 1\cdot 7 \rightarrow x = +7$

2) $\frac{x}{7}=-1$

Solving this one, we find

$\frac{x}{7}\cdot 7 = -1\cdot 7 \rightarrow x = -7$

So the two solutions are +7 and -7.