Algebra Examples

3 (2 x - 3) < (- 5) | 7 - 10 |

$3 (2 x - 3) < (- 5) | 7 - 10 |$

Step 1

Simplify.

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Step 1.1

Subtract

10

$10$ from

7

$7$ .

3 (2 x - 3) < - 5 | - 3 |

$3 (2 x - 3) < - 5 | - 3 |$

Step 1.2

The absolute value is the distance between a number and zero. The distance between

- 3

$- 3$ and

0

$0$ is

3

$3$ .

3 (2 x - 3) < - 5 \cdot 3

$3 (2 x - 3) < - 5 \cdot 3$

Step 1.3

Multiply

- 5

$- 5$ by

3

$3$ .

3 (2 x - 3) < - 15

$3 (2 x - 3) < - 15$

3 (2 x - 3) < - 15

$3 (2 x - 3) < - 15$

Step 2

Divide each term in

3 (2 x - 3) < - 15

$3 (2 x - 3) < - 15$ by

3

$3$ and simplify.

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Step 2.1

Divide each term in

3 (2 x - 3) < - 15

$3 (2 x - 3) < - 15$ by

3

$3$ .

\frac{3 (2 x - 3)}{3} < \frac{- 15}{3}

$\frac{3 (2 x - 3)}{3} < \frac{- 15}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

3

$3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 (2 x - 3)}{3} < \frac{- 15}{3}$

Step 2.2.1.2

Divide

$2 x - 3$ by

$1$ .

$2 x - 3 < \frac{- 15}{3}$

$2 x - 3 < \frac{- 15}{3}$

$2 x - 3 < \frac{- 15}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide

$- 15$ by

$3$ .

$2 x - 3 < - 5$

$2 x - 3 < - 5$

$2 x - 3 < - 5$

Step 3

Move all terms not containing

$x$ to the right side of the inequality.

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Step 3.1

Add

$3$ to both sides of the inequality.

$2 x < - 5 + 3$

Step 3.2

Add

$- 5$ and

$3$ .

$2 x < - 2$

$2 x < - 2$

Step 4

Divide each term in

$2 x < - 2$ by

$2$ and simplify.

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Step 4.1

Divide each term in

$2 x < - 2$ by

$2$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

$2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide

$x$ by

$1$ .

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

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

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide

$- 2$ by

$2$ .

$x < - 1$

$x < - 1$

$x < - 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - 1$

Interval Notation:

$(- \infty, - 1)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$