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Find the Intersection of the Inequalities 2y-3<-7 , 4y+6<30

$2 y - 3 < - 7$ ,

$4 y + 6 < 30$

Step 1

Simplify the first inequality.

Move all terms not containing

$y$ to the right side of the inequality.

Add

$3$ to both sides of the inequality.

$2 y < - 7 + 3$ and

$4 y + 6 < 30$

Add

$- 7$ and

$3$ .

$2 y < - 4$ and

$4 y + 6 < 30$

$2 y < - 4$ and

$4 y + 6 < 30$

Divide each term in

$2 y < - 4$ by

$2$ and simplify.

Divide each term in

$2 y < - 4$ by

$2$ .

$\frac{2 y}{2} < \frac{- 4}{2}$ and

$4 y + 6 < 30$

Simplify the left side.

Cancel the common factor of

$2$ .

Cancel the common factor.

$\frac{2 y}{2} < \frac{- 4}{2}$ and

$4 y + 6 < 30$

Divide

$y$ by

$1$ .

$y < \frac{- 4}{2}$ and

$4 y + 6 < 30$

$y < \frac{- 4}{2}$ and

$4 y + 6 < 30$

$y < \frac{- 4}{2}$ and

$4 y + 6 < 30$

Simplify the right side.

Divide

$- 4$ by

$2$ .

$y < - 2$ and

$4 y + 6 < 30$

$y < - 2$ and

$4 y + 6 < 30$

$y < - 2$ and

$4 y + 6 < 30$

$y < - 2$ and

$4 y + 6 < 30$

Step 2

Simplify the second inequality.

Move all terms not containing

$y$ to the right side of the inequality.

Subtract

$6$ from both sides of the inequality.

$y < - 2$ and

$4 y < 30 - 6$

Subtract

$6$ from

$30$ .

$y < - 2$ and

$4 y < 24$

$y < - 2$ and

$4 y < 24$

Divide each term in

$4 y < 24$ by

$4$ and simplify.

Divide each term in

$4 y < 24$ by

$4$ .

$y < - 2$ and

$\frac{4 y}{4} < \frac{24}{4}$

Simplify the left side.

Cancel the common factor of

$4$ .

Cancel the common factor.

$y < - 2$ and

$\frac{4 y}{4} < \frac{24}{4}$

Divide

$y$ by

$1$ .

$y < - 2$ and

$y < \frac{24}{4}$

$y < - 2$ and

$y < \frac{24}{4}$

$y < - 2$ and

$y < \frac{24}{4}$

Simplify the right side.

Divide

$24$ by

$4$ .

$y < - 2$ and

$y < 6$

$y < - 2$ and

$y < 6$

$y < - 2$ and

$y < 6$

$y < - 2$ and

$y < 6$

Step 3

The intersection consists of the elements that are contained in both intervals.

$y < - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y < - 2$

Interval Notation:

$(- \infty, - 2)$

Step 5

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