Solve for x -10<=3x-4<=2

$- 10 \leq 3 x - 4 \leq 2$

Step 1

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

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 10 + 4 \leq 3 x \leq 2 + 4$

Add $- 10$ and $4$ .

$- 6 \leq 3 x \leq 2 + 4$

Add $2$ and $4$ .

$- 6 \leq 3 x \leq 6$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 6}{3} \leq \frac{3 x}{3} \leq \frac{6}{3}$

Step 3

Divide $- 6$ by $3$ .

$- 2 \leq \frac{3 x}{3} \leq \frac{6}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 2 \leq \frac{3 x}{3} \leq \frac{6}{3}$

Divide $x$ by $1$ .

$- 2 \leq x \leq \frac{6}{3}$

Step 5

Divide $6$ by $3$ .

$- 2 \leq x \leq 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq x \leq 2$

Interval Notation:

$[- 2, 2]$

Step 7