Pre-Algebra Examples

$x + y < - 1$ , $- 2 x + 3 y > 2$

Step 1

Subtract $x$ from both sides of the inequality.

$y < - 1 - x$

Step 2

Solve $- 2 x + 3 y > 2$ for $y$ .

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Step 2.1

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

$3 y > 2 + 2 x$

Step 2.2

Divide each term in $3 y > 2 + 2 x$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 y > 2 + 2 x$ by $3$ .

$\frac{3 y}{3} > \frac{2}{3} + \frac{2 x}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} > \frac{2}{3} + \frac{2 x}{3}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{2}{3} + \frac{2 x}{3}$

Step 3

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

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

Step 4