Precalculus Examples

$- 7 x < x + 7$

Step 1

Move all terms containing $x$ to the left side of the inequality.

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Step 1.1

Subtract $x$ from both sides of the inequality.

$- 7 x - x < 7$

Step 1.2

Subtract $x$ from $- 7 x$ .

$- 8 x < 7$

Step 2

Divide each term in $- 8 x < 7$ by $- 8$ and simplify.

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Step 2.1

Divide each term in $- 8 x < 7$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} > \frac{7}{- 8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} > \frac{7}{- 8}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x > \frac{7}{- 8}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$x > - \frac{7}{8}$

Step 3

Convert the inequality to interval notation.

$(- \frac{7}{8}, \infty)$

Step 4