Algebra Examples

$- 38 \leq - 4 x - 6 < - 26$

Step 1

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

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Step 1.1

Add $6$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 38 + 6 \leq - 4 x < - 26 + 6$

Step 1.2

Add $- 38$ and $6$ .

$- 32 \leq - 4 x < - 26 + 6$

Step 1.3

Add $- 26$ and $6$ .

$- 32 \leq - 4 x < - 20$

Step 2

Divide each term in the inequality by $- 4$ .

$\frac{- 32}{- 4} \geq \frac{- 4 x}{- 4} > \frac{- 20}{- 4}$

Step 3

Divide $- 32$ by $- 4$ .

$8 \geq \frac{- 4 x}{- 4} > \frac{- 20}{- 4}$

Step 4

Cancel the common factor of $- 4$ .

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Step 4.1

Cancel the common factor.

$8 \geq \frac{- 4 x}{- 4} > \frac{- 20}{- 4}$

Step 4.2

Divide $x$ by $1$ .

$8 \geq x > \frac{- 20}{- 4}$

Step 5

Divide $- 20$ by $- 4$ .

$8 \geq x > 5$

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.

$5 < x \leq 8$

Step 7