Solve for y -2.5<=(1-3y)/2<=1.5

$- 2.5 \leq \frac{1 - 3 y}{2} \leq 1.5$

Step 1

Multiply each term in the inequality by $2$ .

$- 2.5 \cdot 2 \leq \frac{1 - 3 y}{2} \cdot 2 \leq 1.5 \cdot 2$

Step 2

Multiply $- 2.5$ by $2$ .

$- 5 \leq \frac{1 - 3 y}{2} \cdot 2 \leq 1.5 \cdot 2$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 \leq \frac{1 - 3 y}{2} \cdot 2 \leq 1.5 \cdot 2$

Rewrite the expression.

$- 5 \leq 1 - 3 y \leq 1.5 \cdot 2$

Step 4

Multiply $1.5$ by $2$ .

$- 5 \leq 1 - 3 y \leq 3$

Step 5

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

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 1 \leq - 3 y \leq 3 - 1$

Subtract $1$ from $- 5$ .

$- 6 \leq - 3 y \leq 3 - 1$

Subtract $1$ from $3$ .

$- 6 \leq - 3 y \leq 2$

Step 6

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

$\frac{- 6}{- 3} \geq \frac{- 3 y}{- 3} \geq \frac{2}{- 3}$

Step 7

Divide $- 6$ by $- 3$ .

$2 \geq \frac{- 3 y}{- 3} \geq \frac{2}{- 3}$

Step 8

Cancel the common factor of $- 3$ .

Cancel the common factor.

$2 \geq \frac{- 3 y}{- 3} \geq \frac{2}{- 3}$

Divide $y$ by $1$ .

$2 \geq y \geq \frac{2}{- 3}$

Step 9

Cancel the common factor of $2$ and $- 3$ .

Rewrite $2$ as $1 (2)$ .

$2 \geq y \geq \frac{1 (2)}{- 3}$

Cancel the common factors.

Rewrite $- 3$ as $1 (- 3)$ .

$2 \geq y \geq \frac{1 \cdot 2}{1 \cdot - 3}$

Cancel the common factor.

$2 \geq y \geq \frac{1 \cdot 2}{1 \cdot - 3}$

Rewrite the expression.

$2 \geq y \geq \frac{2}{- 3}$

Step 10

Move the negative in front of the fraction.

$2 \geq y \geq - \frac{2}{3}$

Step 11

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

$- \frac{2}{3} \leq y \leq 2$

Step 12

The result can be shown in multiple forms.

Inequality Form:

$- \frac{2}{3} \leq y \leq 2$

Interval Notation:

$[- \frac{2}{3}, 2]$

Step 13

Solve for y -2.5<=(1-3y)/2<=1.5

Related Questions

Support LCMGCF.com by disabling your adblocker.