Algebra Examples

5 - x > x + 1

$5 - x > x + 1$

Step 1

Move all terms containing

x

$x$ to the left side of the inequality.

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Step 1.1

Subtract

x

$x$ from both sides of the inequality.

5 - x - x > 1

$5 - x - x > 1$

Step 1.2

Subtract

x

$x$ from

- x

$- x$ .

5 - 2 x > 1

$5 - 2 x > 1$

5 - 2 x > 1

$5 - 2 x > 1$

Step 2

Move all terms not containing

x

$x$ to the right side of the inequality.

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Step 2.1

Subtract

5

$5$ from both sides of the inequality.

- 2 x > 1 - 5

$- 2 x > 1 - 5$

Step 2.2

Subtract

5

$5$ from

1

$1$ .

- 2 x > - 4

$- 2 x > - 4$

- 2 x > - 4

$- 2 x > - 4$

Step 3

Divide each term in

- 2 x > - 4

$- 2 x > - 4$ by

- 2

$- 2$ and simplify.

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Step 3.1

Divide each term in

- 2 x > - 4

$- 2 x > - 4$ by

- 2

$- 2$ . 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}

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide

$x$ by

$1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

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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