Algebra Examples

$- 8 \geq - 5 x + 7 \geq - 33$

Step 1

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

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Step 1.1

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 8 - 7 \geq - 5 x \geq - 33 - 7$

Step 1.2

Subtract $7$ from $- 8$ .

$- 15 \geq - 5 x \geq - 33 - 7$

Step 1.3

Subtract $7$ from $- 33$ .

$- 15 \geq - 5 x \geq - 40$

Step 2

Divide each term in the inequality by $- 5$ .

$\frac{- 15}{- 5} \leq \frac{- 5 x}{- 5} \leq \frac{- 40}{- 5}$

Step 3

Divide $- 15$ by $- 5$ .

$3 \leq \frac{- 5 x}{- 5} \leq \frac{- 40}{- 5}$

Step 4

Cancel the common factor of $- 5$ .

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Step 4.1

Cancel the common factor.

$3 \leq \frac{- 5 x}{- 5} \leq \frac{- 40}{- 5}$

Step 4.2

Divide $x$ by $1$ .

$3 \leq x \leq \frac{- 40}{- 5}$

Step 5

Divide $- 40$ by $- 5$ .

$3 \leq x \leq 8$

Step 6