Algebra Examples

$- 4 \leq 8 - 3 x \leq 6$

Step 1

Solve $4 \geq x \geq \frac{2}{3}$ .

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Step 1.1

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

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Step 1.1.1

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

$- 4 - 8 \leq - 3 x \leq 6 - 8$

Step 1.1.2

Subtract $8$ from $- 4$ .

$- 12 \leq - 3 x \leq 6 - 8$

Step 1.1.3

Subtract $8$ from $6$ .

$- 12 \leq - 3 x \leq - 2$

Step 1.2

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

$\frac{- 12}{- 3} \geq \frac{- 3 x}{- 3} \geq \frac{- 2}{- 3}$

Step 1.3

Divide $- 12$ by $- 3$ .

$4 \geq \frac{- 3 x}{- 3} \geq \frac{- 2}{- 3}$

Step 1.4

Cancel the common factor of $- 3$ .

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Step 1.4.1

Cancel the common factor.

$4 \geq \frac{- 3 x}{- 3} \geq \frac{- 2}{- 3}$

Step 1.4.2

Divide $x$ by $1$ .

$4 \geq x \geq \frac{- 2}{- 3}$

Step 1.5

Dividing two negative values results in a positive value.

$4 \geq x \geq \frac{2}{3}$

Step 1.6

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

$\frac{2}{3} \leq x \leq 4$

Step 2

Use the inequality $\frac{2}{3} \leq x \leq 4$ to build the set notation.

${x | \frac{2}{3} \leq x \leq 4}$

Step 3