Pre-Algebra Examples

$5 - x > x + 1$

Step 1

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

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Subtract $x$ from both sides of the inequality.

$5 - x - x > 1$

Subtract $x$ from $- x$ .

$5 - 2 x > 1$

Step 2

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

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Subtract $5$ from both sides of the inequality.

$- 2 x > 1 - 5$

Subtract $5$ from $1$ .

$- 2 x > - 4$

Step 3

Divide each term in $- 2 x > - 4$ by $- 2$ and simplify.

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Divide each term in $- 2 x > - 4$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{- 4}{- 2}$

Simplify the left side.

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Cancel the common factor of $- 2$ .

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Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{- 4}{- 2}$

Divide $x$ by $1$ .

$x < \frac{- 4}{- 2}$

Simplify the right side.

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Divide $- 4$ by $- 2$ .

$x < 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

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