Pre-Algebra Examples

$- 3 < 2 - x$

Step 1

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

$2 - x > - 3$

Step 2

Move all terms not containing $x$ to the right side of the inequality.

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Step 2.1

Subtract $2$ from both sides of the inequality.

$- x > - 3 - 2$

Step 2.2

Subtract $2$ from $- 3$ .

$- x > - 5$

Step 3

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

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Step 3.1

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.

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

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

Step 3.2.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 5$ by $- 1$ .

$x < 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 5$

Interval Notation:

$(- \infty, 5)$