Pre-Algebra Examples

$3 x + \frac{2}{3} > \frac{4}{5} x - 3$

Step 1

Combine $\frac{4}{5}$ and $x$ .

$3 x + \frac{2}{3} > \frac{4 x}{5} - 3$

Step 2

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

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Step 2.1

Subtract $\frac{4 x}{5}$ from both sides of the inequality.

$3 x + \frac{2}{3} - \frac{4 x}{5} > - 3$

Step 2.2

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$3 x \cdot \frac{5}{5} - \frac{4 x}{5} + \frac{2}{3} > - 3$

Step 2.3

Combine $3 x$ and $\frac{5}{5}$ .

$\frac{3 x \cdot 5}{5} - \frac{4 x}{5} + \frac{2}{3} > - 3$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 x \cdot 5 - 4 x}{5} + \frac{2}{3} > - 3$

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 $x$ out of $3 x \cdot 5 - 4 x$ .

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Step 2.5.1.1.1

Factor $x$ out of $3 x \cdot 5$ .

$\frac{x (3 \cdot 5) - 4 x}{5} + \frac{2}{3} > - 3$

Step 2.5.1.1.2

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

$\frac{x (3 \cdot 5) + x \cdot - 4}{5} + \frac{2}{3} > - 3$

Step 2.5.1.1.3

Factor $x$ out of $x (3 \cdot 5) + x \cdot - 4$ .

$\frac{x (3 \cdot 5 - 4)}{5} + \frac{2}{3} > - 3$

Step 2.5.1.2

Multiply $3$ by $5$ .

$\frac{x (15 - 4)}{5} + \frac{2}{3} > - 3$

Step 2.5.1.3

Subtract $4$ from $15$ .

$\frac{x \cdot 11}{5} + \frac{2}{3} > - 3$

Step 2.5.2

Move $11$ to the left of $x$ .

$\frac{11 x}{5} + \frac{2}{3} > - 3$

Step 3

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

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Step 3.1

Subtract $\frac{2}{3}$ from both sides of the inequality.

$\frac{11 x}{5} > - 3 - \frac{2}{3}$

Step 3.2

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

$\frac{11 x}{5} > - 3 \cdot \frac{3}{3} - \frac{2}{3}$

Step 3.3

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

$\frac{11 x}{5} > \frac{- 3 \cdot 3}{3} - \frac{2}{3}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{11 x}{5} > \frac{- 3 \cdot 3 - 2}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 3$ by $3$ .

$\frac{11 x}{5} > \frac{- 9 - 2}{3}$

Step 3.5.2

Subtract $2$ from $- 9$ .

$\frac{11 x}{5} > \frac{- 11}{3}$

Step 3.6

Move the negative in front of the fraction.

$\frac{11 x}{5} > - \frac{11}{3}$

Step 4

Multiply both sides by $5$ .

$\frac{11 x}{5} \cdot 5 > - \frac{11}{3} \cdot 5$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{11 x}{5} \cdot 5 > - \frac{11}{3} \cdot 5$

Step 5.1.1.2

Rewrite the expression.

$11 x > - \frac{11}{3} \cdot 5$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{11}{3} \cdot 5$ .

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Step 5.2.1.1

Multiply $- \frac{11}{3} \cdot 5$ .

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Step 5.2.1.1.1

Multiply $5$ by $- 1$ .

$11 x > - 5 (\frac{11}{3})$

Step 5.2.1.1.2

Combine $- 5$ and $\frac{11}{3}$ .

$11 x > \frac{- 5 \cdot 11}{3}$

Step 5.2.1.1.3

Multiply $- 5$ by $11$ .

$11 x > \frac{- 55}{3}$

Step 5.2.1.2

Move the negative in front of the fraction.

$11 x > - \frac{55}{3}$

Step 6

Divide each term in $11 x > - \frac{55}{3}$ by $11$ and simplify.

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Step 6.1

Divide each term in $11 x > - \frac{55}{3}$ by $11$ .

$\frac{11 x}{11} > \frac{- \frac{55}{3}}{11}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $11$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{11 x}{11} > \frac{- \frac{55}{3}}{11}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x > \frac{- \frac{55}{3}}{11}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$x > - \frac{55}{3} \cdot \frac{1}{11}$

Step 6.3.2

Cancel the common factor of $11$ .

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Step 6.3.2.1

Move the leading negative in $- \frac{55}{3}$ into the numerator.

$x > \frac{- 55}{3} \cdot \frac{1}{11}$

Step 6.3.2.2

Factor $11$ out of $- 55$ .

$x > \frac{11 (- 5)}{3} \cdot \frac{1}{11}$

Step 6.3.2.3

Cancel the common factor.

$x > \frac{11 \cdot - 5}{3} \cdot \frac{1}{11}$

Step 6.3.2.4

Rewrite the expression.

$x > \frac{- 5}{3}$

Step 6.3.3

Move the negative in front of the fraction.

$x > - \frac{5}{3}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{5}{3}$

Interval Notation:

$(- \frac{5}{3}, \infty)$