Solve for x -14<=3/2x-5<=1

$- 14 \leq \frac{3}{2} x - 5 \leq 1$

Step 1

Combine $\frac{3}{2}$ and $x$ .

$- 14 \leq \frac{3 x}{2} - 5 \leq 1$

Step 2

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

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 14 + 5 \leq \frac{3 x}{2} \leq 1 + 5$

Add $- 14$ and $5$ .

$- 9 \leq \frac{3 x}{2} \leq 1 + 5$

Multiply each term in the inequality by $2$ .

$- 9 \cdot 2 \leq \frac{3 x}{2} \cdot 2 \leq 1 \cdot 2 + 5 \cdot 2$

Multiply $- 9$ by $2$ .

$- 18 \leq \frac{3 x}{2} \cdot 2 \leq 1 \cdot 2 + 5 \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 18 \leq \frac{3 x}{2} \cdot 2 \leq 1 \cdot 2 + 5 \cdot 2$

Rewrite the expression.

$- 18 \leq 3 x \leq 1 \cdot 2 + 5 \cdot 2$

Simplify each term.

Multiply $2$ by $1$ .

$- 18 \leq 3 x \leq 2 + 5 \cdot 2$

Multiply $5$ by $2$ .

$- 18 \leq 3 x \leq 2 + 10$

Add $2$ and $10$ .

$- 18 \leq 3 x \leq 12$

Step 3

Divide each term in the inequality by $3$ .

$\frac{- 18}{3} \leq \frac{3 x}{3} \leq \frac{12}{3}$

Step 4

Divide $- 18$ by $3$ .

$- 6 \leq \frac{3 x}{3} \leq \frac{12}{3}$

Step 5

Cancel the common factor of $3$ .

Cancel the common factor.

$- 6 \leq \frac{3 x}{3} \leq \frac{12}{3}$

Divide $x$ by $1$ .

$- 6 \leq x \leq \frac{12}{3}$

Step 6

Divide $12$ by $3$ .

$- 6 \leq x \leq 4$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 6 \leq x \leq 4$

Interval Notation:

$[- 6, 4]$

Step 8

Solve for x -14<=3/2x-5<=1

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