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 $4 y + 6 < 30$

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 $4 y + 6 < 30$

Simplify the right side.

Divide $- 4$ by $2$ .

$y < - 2$ 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 $4 y < 24$

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

Simplify the right side.

Divide $24$ by $4$ .

$y < - 2$ 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

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

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