Solve the Inequality for y -4<(y-7)/-3<=2

$- 4 < \frac{y - 7}{- 3} \leq 2$

Step 1

Move the negative in front of the fraction.

$- 4 < - \frac{y - 7}{3} \leq 2$

Step 2

Multiply each term in the inequality by $3$ .

$- 4 \cdot 3 < - \frac{y - 7}{3} \cdot 3 \leq 2 \cdot 3$

Step 3

Multiply $- 4$ by $3$ .

$- 12 < - \frac{y - 7}{3} \cdot 3 \leq 2 \cdot 3$

Step 4

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{y - 7}{3}$ into the numerator.

$- 12 < \frac{- (y - 7)}{3} \cdot 3 \leq 2 \cdot 3$

Cancel the common factor.

$- 12 < \frac{- (y - 7)}{3} \cdot 3 \leq 2 \cdot 3$

Rewrite the expression.

$- 12 < - (y - 7) \leq 2 \cdot 3$

Step 5

Apply the distributive property.

$- 12 < - y + 7 \leq 2 \cdot 3$

Step 6

Multiply $2$ by $3$ .

$- 12 < - y + 7 \leq 6$

Step 7

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

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 - 7 < - y \leq 6 - 7$

Subtract $7$ from $- 12$ .

$- 19 < - y \leq 6 - 7$

Subtract $7$ from $6$ .

$- 19 < - y \leq - 1$

Step 8

Multiply each term in the inequality by $- 1$ .

$\frac{- 19}{- 1} > \frac{- y}{- 1} \geq \frac{- 1}{- 1}$

Step 9

Divide $- 19$ by $- 1$ .

$19 > \frac{- y}{- 1} \geq \frac{- 1}{- 1}$

Step 10

Dividing two negative values results in a positive value.

$19 > \frac{y}{1} \geq \frac{- 1}{- 1}$

Step 11

Divide $y$ by $1$ .

$19 > y \geq \frac{- 1}{- 1}$

Step 12

Divide $- 1$ by $- 1$ .

$19 > y \geq 1$

Step 13

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

$1 \leq y < 19$

Step 14

The result can be shown in multiple forms.

Inequality Form:

$1 \leq y < 19$

Interval Notation:

$[1, 19)$

Step 15

Solve the Inequality for y -4<(y-7)/-3<=2

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