Pre-Algebra Examples

$- \frac{3}{8} \cdot (16 x - 8) > 4$

Step 1

Multiply each term in $- \frac{3}{8} \cdot (16 x - 8) > 4$ by $- \frac{8}{3}$ to eliminate the fractions.

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Step 1.1

Multiply each term in $- \frac{3}{8} \cdot (16 x - 8) > 4$ by $- \frac{8}{3}$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{3}{8} \cdot (16 x - 8) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2

Simplify the left side.

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Step 1.2.1

Apply the distributive property.

$(- \frac{3}{8} (16 x) - \frac{3}{8} \cdot - 8) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.2

Cancel the common factor of $8$ .

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Step 1.2.2.1

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$(\frac{- 3}{8} (16 x) - \frac{3}{8} \cdot - 8) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.2.2

Factor $8$ out of $16 x$ .

$(\frac{- 3}{8} (8 (2 x)) - \frac{3}{8} \cdot - 8) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.2.3

Cancel the common factor.

$(\frac{- 3}{8} (8 (2 x)) - \frac{3}{8} \cdot - 8) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.2.4

Rewrite the expression.

$(- 3 (2 x) - \frac{3}{8} \cdot - 8) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.3

Multiply $2$ by $- 3$ .

$(- 6 x - \frac{3}{8} \cdot - 8) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.4

Cancel the common factor of $8$ .

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Step 1.2.4.1

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$(- 6 x + \frac{- 3}{8} \cdot - 8) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.4.2

Factor $8$ out of $- 8$ .

$(- 6 x + \frac{- 3}{8} \cdot (8 (- 1))) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.4.3

Cancel the common factor.

$(- 6 x + \frac{- 3}{8} \cdot (8 \cdot - 1)) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.4.4

Rewrite the expression.

$(- 6 x - 3 \cdot - 1) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.5

Multiply $- 3$ by $- 1$ .

$(- 6 x + 3) (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.6

Apply the distributive property.

$- 6 x (- \frac{8}{3}) + 3 (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.7

Cancel the common factor of $3$ .

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Step 1.2.7.1

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$- 6 x \frac{- 8}{3} + 3 (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.7.2

Factor $3$ out of $- 6 x$ .

$3 (- 2 x) \frac{- 8}{3} + 3 (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.7.3

Cancel the common factor.

$3 (- 2 x) \frac{- 8}{3} + 3 (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.7.4

Rewrite the expression.

$- 2 x \cdot - 8 + 3 (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.8

Multiply $- 8$ by $- 2$ .

$16 x + 3 (- \frac{8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.9

Cancel the common factor of $3$ .

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Step 1.2.9.1

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$16 x + 3 (\frac{- 8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.9.2

Cancel the common factor.

$16 x + 3 (\frac{- 8}{3}) < 4 (- \frac{8}{3})$

Step 1.2.9.3

Rewrite the expression.

$16 x - 8 < 4 (- \frac{8}{3})$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply $4 (- \frac{8}{3})$ .

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Step 1.3.1.1

Multiply $- 1$ by $4$ .

$16 x - 8 < - 4 (\frac{8}{3})$

Step 1.3.1.2

Combine $- 4$ and $\frac{8}{3}$ .

$16 x - 8 < \frac{- 4 \cdot 8}{3}$

Step 1.3.1.3

Multiply $- 4$ by $8$ .

$16 x - 8 < \frac{- 32}{3}$

Step 1.3.2

Move the negative in front of the fraction.

$16 x - 8 < - \frac{32}{3}$

Step 2

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

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Step 2.1

Add $8$ to both sides of the inequality.

$16 x < - \frac{32}{3} + 8$

Step 2.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$16 x < - \frac{32}{3} + 8 \cdot \frac{3}{3}$

Step 2.3

Combine $8$ and $\frac{3}{3}$ .

$16 x < - \frac{32}{3} + \frac{8 \cdot 3}{3}$

Step 2.4

Combine the numerators over the common denominator.

$16 x < \frac{- 32 + 8 \cdot 3}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $8$ by $3$ .

$16 x < \frac{- 32 + 24}{3}$

Step 2.5.2

Add $- 32$ and $24$ .

$16 x < \frac{- 8}{3}$

Step 2.6

Move the negative in front of the fraction.

$16 x < - \frac{8}{3}$

Step 3

Divide each term in $16 x < - \frac{8}{3}$ by $16$ and simplify.

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Step 3.1

Divide each term in $16 x < - \frac{8}{3}$ by $16$ .

$\frac{16 x}{16} < \frac{- \frac{8}{3}}{16}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $16$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{16 x}{16} < \frac{- \frac{8}{3}}{16}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{- \frac{8}{3}}{16}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x < - \frac{8}{3} \cdot \frac{1}{16}$

Step 3.3.2

Cancel the common factor of $8$ .

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Step 3.3.2.1

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$x < \frac{- 8}{3} \cdot \frac{1}{16}$

Step 3.3.2.2

Factor $8$ out of $- 8$ .

$x < \frac{8 (- 1)}{3} \cdot \frac{1}{16}$

Step 3.3.2.3

Factor $8$ out of $16$ .

$x < \frac{8 \cdot - 1}{3} \cdot \frac{1}{8 \cdot 2}$

Step 3.3.2.4

Cancel the common factor.

$x < \frac{8 \cdot - 1}{3} \cdot \frac{1}{8 \cdot 2}$

Step 3.3.2.5

Rewrite the expression.

$x < \frac{- 1}{3} \cdot \frac{1}{2}$

Step 3.3.3

Multiply $\frac{- 1}{3}$ by $\frac{1}{2}$ .

$x < \frac{- 1}{3 \cdot 2}$

Step 3.3.4

Simplify the expression.

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Step 3.3.4.1

Multiply $3$ by $2$ .

$x < \frac{- 1}{6}$

Step 3.3.4.2

Move the negative in front of the fraction.

$x < - \frac{1}{6}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{1}{6}$

Interval Notation:

$(- \infty, - \frac{1}{6})$