Solve for y -10<5-3y<=2

$- 10 < 5 - 3 y \leq 2$

Step 1

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

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

$- 10 - 5 < - 3 y \leq 2 - 5$

Subtract $5$ from $- 10$ .

$- 15 < - 3 y \leq 2 - 5$

Subtract $5$ from $2$ .

$- 15 < - 3 y \leq - 3$

Step 2

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

$\frac{- 15}{- 3} > \frac{- 3 y}{- 3} \geq \frac{- 3}{- 3}$

Step 3

Divide $- 15$ by $- 3$ .

$5 > \frac{- 3 y}{- 3} \geq \frac{- 3}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$5 > \frac{- 3 y}{- 3} \geq \frac{- 3}{- 3}$

Divide $y$ by $1$ .

$5 > y \geq \frac{- 3}{- 3}$

Step 5

Divide $- 3$ by $- 3$ .

$5 > y \geq 1$

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.

$1 \leq y < 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$1 \leq y < 5$

Interval Notation:

$[1, 5)$

Step 8