Algebra Examples

$4 > 4 x - y$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite so $y$ is on the left side of the inequality.

$4 x - y < 4$

Step 1.2

Subtract $4 x$ from both sides of the inequality.

$- y < 4 - 4 x$

Step 1.3

Divide each term in $- y < 4 - 4 x$ by $- 1$ and simplify.

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Step 1.3.1

Divide each term in $- y < 4 - 4 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{4}{- 1} + \frac{- 4 x}{- 1}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{4}{- 1} + \frac{- 4 x}{- 1}$

Step 1.3.2.2

Divide $y$ by $1$ .

$y > \frac{4}{- 1} + \frac{- 4 x}{- 1}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide $4$ by $- 1$ .

$y > - 4 + \frac{- 4 x}{- 1}$

Step 1.3.3.1.2

Move the negative one from the denominator of $\frac{- 4 x}{- 1}$ .

$y > - 4 - 1 \cdot (- 4 x)$

Step 1.3.3.1.3

Rewrite $- 1 \cdot (- 4 x)$ as $- (- 4 x)$ .

$y > - 4 - (- 4 x)$

Step 1.3.3.1.4

Multiply $- 4$ by $- 1$ .

$y > - 4 + 4 x$

Step 2

Rearrange terms.

$y > 4 x - 4$