Solve the System of Inequalities 9y-2<13 and 3y-2>-29

$9 y - 2 < 13$ and $3 y - 2 > - 29$

Step 1

Simplify the first inequality.

Move all terms not containing $y$ to the right side of the inequality.

Add $2$ to both sides of the inequality.

$9 y < 13 + 2$ and $3 y - 2 > - 29$

Add $13$ and $2$ .

$9 y < 15$ and $3 y - 2 > - 29$

Divide each term in $9 y < 15$ by $9$ and simplify.

Divide each term in $9 y < 15$ by $9$ .

$\frac{9 y}{9} < \frac{15}{9}$ and $3 y - 2 > - 29$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} < \frac{15}{9}$ and $3 y - 2 > - 29$

Divide $y$ by $1$ .

$y < \frac{15}{9}$ and $3 y - 2 > - 29$

Simplify the right side.

Cancel the common factor of $15$ and $9$ .

Factor $3$ out of $15$ .

$y < \frac{3 (5)}{9}$ and $3 y - 2 > - 29$

Cancel the common factors.

Factor $3$ out of $9$ .

$y < \frac{3 \cdot 5}{3 \cdot 3}$ and $3 y - 2 > - 29$

Cancel the common factor.

$y < \frac{3 \cdot 5}{3 \cdot 3}$ and $3 y - 2 > - 29$

Rewrite the expression.

$y < \frac{5}{3}$ and $3 y - 2 > - 29$

Step 2

Simplify the second inequality.

Move all terms not containing $y$ to the right side of the inequality.

Add $2$ to both sides of the inequality.

$y < \frac{5}{3}$ and $3 y > - 29 + 2$

Add $- 29$ and $2$ .

$y < \frac{5}{3}$ and $3 y > - 27$

Divide each term in $3 y > - 27$ by $3$ and simplify.

Divide each term in $3 y > - 27$ by $3$ .

$y < \frac{5}{3}$ and $\frac{3 y}{3} > \frac{- 27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$y < \frac{5}{3}$ and $\frac{3 y}{3} > \frac{- 27}{3}$

Divide $y$ by $1$ .

$y < \frac{5}{3}$ and $y > \frac{- 27}{3}$

Simplify the right side.

Divide $- 27$ by $3$ .

$y < \frac{5}{3}$ and $y > - 9$

Step 3

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

$- 9 < y < \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 9 < y < \frac{5}{3}$

Interval Notation:

$(- 9, \frac{5}{3})$

Step 5

Solve the System of Inequalities 9y-2<13 and 3y-2>-29

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