Algebra Examples

$2 x - y < 3$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $2 x$ from both sides of the inequality.

$- y < 3 - 2 x$

Step 1.2

Divide each term in $- y < 3 - 2 x$ by $- 1$ and simplify.

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Step 1.2.1

Divide each term in $- y < 3 - 2 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.2.2.2

Divide $y$ by $1$ .

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $3$ by $- 1$ .

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

Step 1.2.3.1.2

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y > - 3 - 1 \cdot (- 2 x)$

Step 1.2.3.1.3

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y > - 3 - (- 2 x)$

Step 1.2.3.1.4

Multiply $- 2$ by $- 1$ .

$y > - 3 + 2 x$

Step 2

Rearrange terms.

$y > 2 x - 3$