Algebra Examples

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

Step 1

Simplify.

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Step 1.1

Subtract $10$ from $7$ .

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

Step 1.2

The absolute value is the distance between a number and zero. The distance between $- 3$ and $0$ is $3$ .

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

Step 1.3

Multiply $- 5$ by $3$ .

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

Step 2

Divide each term in $3 (2 x - 3) < - 15$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 (2 x - 3) < - 15$ by $3$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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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 $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 15$ by $3$ .

$2 x - 3 < - 5$

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 $3$ .

$2 x < - 2$

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 $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 2$ by $2$ .

$x < - 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - 1$

Interval Notation:

$(- \infty, - 1)$