Questions: -7x+8 = 7 -15/7, -1/7 1/7 1/7, 15/7 15/7, -1/7

Transcript text: \[ |-7 x+8|=7 \] $\left\{-\frac{15}{7},-\frac{1}{7}\right\}$ $\left\{\frac{1}{7}\right\}$ $\left\{\frac{1}{7}, \frac{15}{7}\right\}$ $\left\{\frac{15}{7},-\frac{1}{7}\right\}$

Solution

Solution Steps

Step 1: Understand the Absolute Value Equation

The equation given is: \[ |-7x + 8| = 7 \] The absolute value equation $ |A| = B $ implies that $ A = B $ or $ A = -B $. Therefore, we can split the equation into two cases:

$ -7x + 8 = 7 $
$ -7x + 8 = -7 $

Step 2: Solve the First Case

Solve $ -7x + 8 = 7 $: \[ -7x + 8 = 7 \] Subtract 8 from both sides: \[ -7x = 7 - 8 \] \[ -7x = -1 \] Divide both sides by $-7$: \[ x = \frac{-1}{-7} = \frac{1}{7} \]

Step 3: Solve the Second Case

Solve $ -7x + 8 = -7 $: \[ -7x + 8 = -7 \] Subtract 8 from both sides: \[ -7x = -7 - 8 \] \[ -7x = -15 \] Divide both sides by $-7$: \[ x = \frac{-15}{-7} = \frac{15}{7} \]