Precalculus Examples

$- 10 \leq - 3 x + 3 < - 5$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 10 - 3 \leq - 3 x < - 5 - 3$

Step 1.2

Subtract $3$ from $- 10$ .

$- 13 \leq - 3 x < - 5 - 3$

Step 1.3

Subtract $3$ from $- 5$ .

$- 13 \leq - 3 x < - 8$

Step 2

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

$\frac{- 13}{- 3} \geq \frac{- 3 x}{- 3} > \frac{- 8}{- 3}$

Step 3

Dividing two negative values results in a positive value.

$\frac{13}{3} \geq \frac{- 3 x}{- 3} > \frac{- 8}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

$\frac{13}{3} \geq \frac{- 3 x}{- 3} > \frac{- 8}{- 3}$

Step 4.2

Divide $x$ by $1$ .

$\frac{13}{3} \geq x > \frac{- 8}{- 3}$

Step 5

Dividing two negative values results in a positive value.

$\frac{13}{3} \geq x > \frac{8}{3}$

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.

$\frac{8}{3} < x \leq \frac{13}{3}$

Step 7

Convert the inequality to interval notation.

$(\frac{8}{3}, \frac{13}{3}]$

Step 8