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

x = +7, x = -7

Step-by-step explanation:

The equation to solve is:

`\left|(x)/(7)\right|=1`

Which means that the absolute value of the fraction
`(x)/(7)` must be equal to 1. Since we have an absolute value, we have basically two equations to solve:

1)
`(x)/(7)=+1`

Solving this one, we find

`(x)/(7)\cdot 7 = 1\cdot 7 \rightarrow x = +7`

2)
`(x)/(7)=-1`

Solving this one, we find

`(x)/(7)\cdot 7 = -1\cdot 7 \rightarrow x = -7`

So the two solutions are +7 and -7.