Solve for x -7<=(-8x+9)/9<=2

$- 7 \leq \frac{- 8 x + 9}{9} \leq 2$

Factor $- 1$ out of $- 8 x$ .

$- 7 \leq \frac{- (8 x) + 9}{9} \leq 2$

Rewrite $9$ as $- 1 (- 9)$ .

$- 7 \leq \frac{- (8 x) - 1 \cdot - 9}{9} \leq 2$

Factor $- 1$ out of $- (8 x) - 1 (- 9)$ .

$- 7 \leq \frac{- (8 x - 9)}{9} \leq 2$

Simplify the expression.

Rewrite $- (8 x - 9)$ as $- 1 (8 x - 9)$ .

$- 7 \leq \frac{- 1 (8 x - 9)}{9} \leq 2$

Move the negative in front of the fraction.

$- 7 \leq - \frac{8 x - 9}{9} \leq 2$

Multiply each term in the inequality by $9$ .

$- 7 \cdot 9 \leq - \frac{8 x - 9}{9} \cdot 9 \leq 2 \cdot 9$

Multiply $- 7$ by $9$ .

$- 63 \leq - \frac{8 x - 9}{9} \cdot 9 \leq 2 \cdot 9$

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{8 x - 9}{9}$ into the numerator.

$- 63 \leq \frac{- (8 x - 9)}{9} \cdot 9 \leq 2 \cdot 9$

Cancel the common factor.

$- 63 \leq \frac{- (8 x - 9)}{9} \cdot 9 \leq 2 \cdot 9$

Rewrite the expression.

$- 63 \leq - (8 x - 9) \leq 2 \cdot 9$

Apply the distributive property.

$- 63 \leq - (8 x) + 9 \leq 2 \cdot 9$

Multiply.

Multiply $8$ by $- 1$ .

$- 63 \leq - 8 x + 9 \leq 2 \cdot 9$

Multiply $- 1$ by $- 9$ .

$- 63 \leq - 8 x + 9 \leq 2 \cdot 9$

Multiply $2$ by $9$ .

$- 63 \leq - 8 x + 9 \leq 18$

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

Subtract $9$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 63 - 9 \leq - 8 x \leq 18 - 9$

Subtract $9$ from $- 63$ .

$- 72 \leq - 8 x \leq 18 - 9$

Subtract $9$ from $18$ .

$- 72 \leq - 8 x \leq 9$

Divide each term in the inequality by $- 8$ .

$\frac{- 72}{- 8} \geq \frac{- 8 x}{- 8} \geq \frac{9}{- 8}$

Divide $- 72$ by $- 8$ .

$9 \geq \frac{- 8 x}{- 8} \geq \frac{9}{- 8}$

Cancel the common factor of $- 8$ .

Cancel the common factor.

$9 \geq \frac{- 8 x}{- 8} \geq \frac{9}{- 8}$

Divide $x$ by $1$ .

$9 \geq x \geq \frac{9}{- 8}$

Move the negative in front of the fraction.

$9 \geq x \geq - \frac{9}{8}$

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

$- \frac{9}{8} \leq x \leq 9$

The result can be shown in multiple forms.

Inequality Form:

$- \frac{9}{8} \leq x \leq 9$

Interval Notation:

$[- \frac{9}{8}, 9]$

Solve for x -7<=(-8x+9)/9<=2

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