Pre-Algebra Examples

$- 4 x - 5 < - \frac{4}{3} x + 9$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{4}{3}$ .

$- 4 x - 5 < - \frac{x \cdot 4}{3} + 9$

Step 1.2

Move $4$ to the left of $x$ .

$- 4 x - 5 < - \frac{4 x}{3} + 9$

Step 2

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

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Step 2.1

Add $\frac{4 x}{3}$ to both sides of the inequality.

$- 4 x - 5 + \frac{4 x}{3} < 9$

Step 2.2

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 4 x \cdot \frac{3}{3} + \frac{4 x}{3} - 5 < 9$

Step 2.3

Combine $- 4 x$ and $\frac{3}{3}$ .

$\frac{- 4 x \cdot 3}{3} + \frac{4 x}{3} - 5 < 9$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 4 x \cdot 3 + 4 x}{3} - 5 < 9$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $4 x$ out of $- 4 x \cdot 3 + 4 x$ .

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Step 2.5.1.1.1

Factor $4 x$ out of $- 4 x \cdot 3$ .

$\frac{4 x (- 1 \cdot 3) + 4 x}{3} - 5 < 9$

Step 2.5.1.1.2

Factor $4 x$ out of $4 x$ .

$\frac{4 x (- 1 \cdot 3) + 4 x (1)}{3} - 5 < 9$

Step 2.5.1.1.3

Factor $4 x$ out of $4 x (- 1 \cdot 3) + 4 x (1)$ .

$\frac{4 x (- 1 \cdot 3 + 1)}{3} - 5 < 9$

Step 2.5.1.2

Multiply $- 1$ by $3$ .

$\frac{4 x (- 3 + 1)}{3} - 5 < 9$

Step 2.5.1.3

Add $- 3$ and $1$ .

$\frac{4 x \cdot - 2}{3} - 5 < 9$

Step 2.5.1.4

Multiply $- 2$ by $4$ .

$\frac{- 8 x}{3} - 5 < 9$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{8 x}{3} - 5 < 9$

Step 3

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

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Step 3.1

Add $5$ to both sides of the inequality.

$- \frac{8 x}{3} < 9 + 5$

Step 3.2

Add $9$ and $5$ .

$- \frac{8 x}{3} < 14$

Step 4

Divide each term in $- \frac{8 x}{3} < 14$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- \frac{8 x}{3} < 14$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{8 x}{3}}{- 1} > \frac{14}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{8 x}{3}}{1} > \frac{14}{- 1}$

Step 4.2.2

Divide $\frac{8 x}{3}$ by $1$ .

$\frac{8 x}{3} > \frac{14}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $14$ by $- 1$ .

$\frac{8 x}{3} > - 14$

Step 5

Multiply both sides by $3$ .

$\frac{8 x}{3} \cdot 3 > - 14 \cdot 3$

Step 6

Simplify.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1

Cancel the common factor.

$\frac{8 x}{3} \cdot 3 > - 14 \cdot 3$

Step 6.1.1.2

Rewrite the expression.

$8 x > - 14 \cdot 3$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 14$ by $3$ .

$8 x > - 42$

Step 7

Divide each term in $8 x > - 42$ by $8$ and simplify.

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Step 7.1

Divide each term in $8 x > - 42$ by $8$ .

$\frac{8 x}{8} > \frac{- 42}{8}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $8$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{8 x}{8} > \frac{- 42}{8}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 42}{8}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Cancel the common factor of $- 42$ and $8$ .

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Step 7.3.1.1

Factor $2$ out of $- 42$ .

$x > \frac{2 (- 21)}{8}$

Step 7.3.1.2

Cancel the common factors.

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Step 7.3.1.2.1

Factor $2$ out of $8$ .

$x > \frac{2 \cdot - 21}{2 \cdot 4}$

Step 7.3.1.2.2

Cancel the common factor.

$x > \frac{2 \cdot - 21}{2 \cdot 4}$

Step 7.3.1.2.3

Rewrite the expression.

$x > \frac{- 21}{4}$

Step 7.3.2

Move the negative in front of the fraction.

$x > - \frac{21}{4}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{21}{4}$

Interval Notation:

$(- \frac{21}{4}, \infty)$