Precalculus Examples

$x - 7 y < 7$ , $7 x + y > 7$

Step 1

Add $7 y$ to both sides of the inequality.

$x < 7 + 7 y$ or $7 x + y > 7$

Step 2

Simplify the second inequality.

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Step 2.1

Subtract $y$ from both sides of the inequality.

$x < 7 + 7 y$ or $7 x > 7 - y$

Step 2.2

Divide each term in $7 x > 7 - y$ by $7$ and simplify.

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Step 2.2.1

Divide each term in $7 x > 7 - y$ by $7$ .

$x < 7 + 7 y$ or $\frac{7 x}{7} > \frac{7}{7} + \frac{- y}{7}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $7$ .

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Step 2.2.2.1.1

Cancel the common factor.

$x < 7 + 7 y$ or $\frac{7 x}{7} > \frac{7}{7} + \frac{- y}{7}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x < 7 + 7 y$ or $x > \frac{7}{7} + \frac{- y}{7}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Divide $7$ by $7$ .

$x < 7 + 7 y$ or $x > 1 + \frac{- y}{7}$

Step 2.2.3.1.2

Move the negative in front of the fraction.

$x < 7 + 7 y$ or $x > 1 - \frac{y}{7}$

Step 3