Solve for x -7<=8-3x<=7

$- 7 \leq 8 - 3 x \leq 7$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Subtract $8$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 7 - 8 \leq - 3 x \leq 7 - 8$

Subtract $8$ from $- 7$ .

$- 15 \leq - 3 x \leq 7 - 8$

Subtract $8$ from $7$ .

$- 15 \leq - 3 x \leq - 1$

Step 2

Divide each term in the inequality by $- 3$ .

$\frac{- 15}{- 3} \geq \frac{- 3 x}{- 3} \geq \frac{- 1}{- 3}$

Step 3

Divide $- 15$ by $- 3$ .

$5 \geq \frac{- 3 x}{- 3} \geq \frac{- 1}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$5 \geq \frac{- 3 x}{- 3} \geq \frac{- 1}{- 3}$

Divide $x$ by $1$ .

$5 \geq x \geq \frac{- 1}{- 3}$

Step 5

Dividing two negative values results in a positive value.

$5 \geq x \geq \frac{1}{3}$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$\frac{1}{3} \leq x \leq 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$\frac{1}{3} \leq x \leq 5$

Interval Notation:

$[\frac{1}{3}, 5]$

Step 8