Precalculus Examples

$0 < 5 - x$

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

$5 - x > 0$

Subtract $5$ from both sides of the inequality.

$- x > - 5$

Divide each term in $- x > - 5$ by $- 1$ and simplify.

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Divide each term in $- x > - 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{- 5}{- 1}$

Simplify the left side.

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Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{- 5}{- 1}$

Divide $x$ by $1$ .

$x < \frac{- 5}{- 1}$

Simplify the right side.

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Divide $- 5$ by $- 1$ .

$x < 5$

Convert the inequality to interval notation.

$(- \infty, 5)$