Pre-Algebra Examples

$- 3 (4 x - 8.2) < - 11.98 x + 14 \frac{3}{4}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $- 3 (4 x - 8.2)$ .

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Step 1.1.1

Apply the distributive property.

$- 3 (4 x) - 3 \cdot - 8.2 < - 11.98 x + 14 \frac{3}{4}$

Step 1.1.2

Multiply.

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Step 1.1.2.1

Multiply $4$ by $- 3$ .

$- 12 x - 3 \cdot - 8.2 < - 11.98 x + 14 \frac{3}{4}$

Step 1.1.2.2

Multiply $- 3$ by $- 8.2$ .

$- 12 x + 24.6 < - 11.98 x + 14 \frac{3}{4}$

Step 2

Simplify the right side.

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Step 2.1

Convert $14 \frac{3}{4}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$- 12 x + 24.6 < - 11.98 x + 14 + \frac{3}{4}$

Step 2.1.2

Add $14$ and $\frac{3}{4}$ .

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Step 2.1.2.1

To write $14$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 12 x + 24.6 < - 11.98 x + 14 \cdot \frac{4}{4} + \frac{3}{4}$

Step 2.1.2.2

Combine $14$ and $\frac{4}{4}$ .

$- 12 x + 24.6 < - 11.98 x + \frac{14 \cdot 4}{4} + \frac{3}{4}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$- 12 x + 24.6 < - 11.98 x + \frac{14 \cdot 4 + 3}{4}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $14$ by $4$ .

$- 12 x + 24.6 < - 11.98 x + \frac{56 + 3}{4}$

Step 2.1.2.4.2

Add $56$ and $3$ .

$- 12 x + 24.6 < - 11.98 x + \frac{59}{4}$

Step 3

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

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Step 3.1

Add $11.98 x$ to both sides of the inequality.

$- 12 x + 24.6 + 11.98 x < \frac{59}{4}$

Step 3.2

Add $- 12 x$ and $11.98 x$ .

$- 0.02 x + 24.6 < \frac{59}{4}$

Step 4

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

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Step 4.1

Subtract $24.6$ from both sides of the inequality.

$- 0.02 x < \frac{59}{4} - 24.6$

Step 4.2

To write $- 24.6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 0.02 x < \frac{59}{4} - 24.6 \cdot \frac{4}{4}$

Step 4.3

Combine $- 24.6$ and $\frac{4}{4}$ .

$- 0.02 x < \frac{59}{4} + \frac{- 24.6 \cdot 4}{4}$

Step 4.4

Combine the numerators over the common denominator.

$- 0.02 x < \frac{59 - 24.6 \cdot 4}{4}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 24.6$ by $4$ .

$- 0.02 x < \frac{59 - 98.4}{4}$

Step 4.5.2

Subtract $98.4$ from $59$ .

$- 0.02 x < \frac{- 39.4}{4}$

Step 4.6

Divide $- 39.4$ by $4$ .

$- 0.02 x < - 9.85$

Step 5

Divide each term in $- 0.02 x < - 9.85$ by $- 0.02$ and simplify.

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Step 5.1

Divide each term in $- 0.02 x < - 9.85$ by $- 0.02$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 0.02 x}{- 0.02} > \frac{- 9.85}{- 0.02}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 0.02$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 0.02 x}{- 0.02} > \frac{- 9.85}{- 0.02}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 9.85}{- 0.02}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 9.85$ by $- 0.02$ .

$x > 492.5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 492.5$

Interval Notation:

$(492.5, \infty)$