Algebra Examples

$4 x + 4 y < 16$ $x > y + 16$

Step 1

Solve $4 x + 4 y < 16$ for $y$ .

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Step 1.1

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

$4 y < 16 - 4 x$

Step 1.2

Divide each term in $4 y < 16 - 4 x$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 y < 16 - 4 x$ by $4$ .

$\frac{4 y}{4} < \frac{16}{4} + \frac{- 4 x}{4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} < \frac{16}{4} + \frac{- 4 x}{4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{16}{4} + \frac{- 4 x}{4}$

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 $16$ by $4$ .

$y < 4 + \frac{- 4 x}{4}$

Step 1.2.3.1.2

Cancel the common factor of $- 4$ and $4$ .

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Step 1.2.3.1.2.1

Factor $4$ out of $- 4 x$ .

$y < 4 + \frac{4 (- x)}{4}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $4$ out of $4$ .

$y < 4 + \frac{4 (- x)}{4 (1)}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y < 4 + \frac{4 (- x)}{4 \cdot 1}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

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

Step 1.2.3.1.2.2.4

Divide $- x$ by $1$ .

$y < 4 - x$

Step 2

Solve $x > y + 16$ for $y$ .

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Step 2.1

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

$y + 16 < x$

Step 2.2

Subtract $16$ from both sides of the inequality.

$y < x - 16$

Step 3

Find the intersection of $y < 4 - x$ and $y < x - 16$ .

$y < N o (Min i m u m)$

Step 4