Solve for y 3y<5-2y<7+y

$3 y < 5 - 2 y < 7 + y$

Step 1

Solve $3 y < 5 - 2 y$ for $y$ .

Move all terms containing $y$ to the left side of the inequality.

Add $2 y$ to both sides of the inequality.

$3 y + 2 y < 5$

Add $3 y$ and $2 y$ .

$5 y < 5$

Divide each term in $5 y < 5$ by $5$ and simplify.

Divide each term in $5 y < 5$ by $5$ .

$\frac{5 y}{5} < \frac{5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} < \frac{5}{5}$

Divide $y$ by $1$ .

$y < \frac{5}{5}$

Simplify the right side.

Divide $5$ by $5$ .

$y < 1$

Step 2

Solve $5 - 2 y < 7 + y$ for $y$ .

Move all terms containing $y$ to the left side of the inequality.

Subtract $y$ from both sides of the inequality.

$5 - 2 y - y < 7$

Subtract $y$ from $- 2 y$ .

$5 - 3 y < 7$

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

Subtract $5$ from both sides of the inequality.

$- 3 y < 7 - 5$

Subtract $5$ from $7$ .

$- 3 y < 2$

Divide each term in $- 3 y < 2$ by $- 3$ and simplify.

Divide each term in $- 3 y < 2$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 3

Find the intersection of $y < 1$ and $y > - \frac{2}{3}$ .

$- \frac{2}{3} < y < 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- \frac{2}{3} < y < 1$

Interval Notation:

$(- \frac{2}{3}, 1)$

Step 5

Solve for y 3y<5-2y<7+y

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