Algebra Examples

$- \frac{1}{3} x - 9 > 1.5 - \frac{4}{5} x$

Step 1

Combine $x$ and $\frac{1}{3}$ .

$- \frac{x}{3} - 9 > 1.5 - \frac{4}{5} x$

Step 2

Simplify each term.

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Step 2.1

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

$- \frac{x}{3} - 9 > 1.5 - \frac{x \cdot 4}{5}$

Step 2.2

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

$- \frac{x}{3} - 9 > 1.5 - \frac{4 x}{5}$

Step 3

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

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Step 3.1

Add $\frac{4 x}{5}$ to both sides of the inequality.

$- \frac{x}{3} - 9 + \frac{4 x}{5} > 1.5$

Step 3.2

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

$- \frac{x}{3} \cdot \frac{5}{5} + \frac{4 x}{5} - 9 > 1.5$

Step 3.3

To write $\frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{x}{3} \cdot \frac{5}{5} + \frac{4 x}{5} \cdot \frac{3}{3} - 9 > 1.5$

Step 3.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{x}{3}$ by $\frac{5}{5}$ .

$- \frac{x \cdot 5}{3 \cdot 5} + \frac{4 x}{5} \cdot \frac{3}{3} - 9 > 1.5$

Step 3.4.2

Multiply $3$ by $5$ .

$- \frac{x \cdot 5}{15} + \frac{4 x}{5} \cdot \frac{3}{3} - 9 > 1.5$

Step 3.4.3

Multiply $\frac{4 x}{5}$ by $\frac{3}{3}$ .

$- \frac{x \cdot 5}{15} + \frac{4 x \cdot 3}{5 \cdot 3} - 9 > 1.5$

Step 3.4.4

Multiply $5$ by $3$ .

$- \frac{x \cdot 5}{15} + \frac{4 x \cdot 3}{15} - 9 > 1.5$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- x \cdot 5 + 4 x \cdot 3}{15} - 9 > 1.5$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

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

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Step 3.6.1.1.1

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

$\frac{x (- 1 \cdot 5) + 4 x \cdot 3}{15} - 9 > 1.5$

Step 3.6.1.1.2

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

$\frac{x (- 1 \cdot 5) + x (4 \cdot 3)}{15} - 9 > 1.5$

Step 3.6.1.1.3

Factor $x$ out of $x (- 1 \cdot 5) + x (4 \cdot 3)$ .

$\frac{x (- 1 \cdot 5 + 4 \cdot 3)}{15} - 9 > 1.5$

Step 3.6.1.2

Multiply $- 1$ by $5$ .

$\frac{x (- 5 + 4 \cdot 3)}{15} - 9 > 1.5$

Step 3.6.1.3

Multiply $4$ by $3$ .

$\frac{x (- 5 + 12)}{15} - 9 > 1.5$

Step 3.6.1.4

Add $- 5$ and $12$ .

$\frac{x \cdot 7}{15} - 9 > 1.5$

Step 3.6.2

Move $7$ to the left of $x$ .

$\frac{7 x}{15} - 9 > 1.5$

Step 4

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

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Step 4.1

Add $9$ to both sides of the inequality.

$\frac{7 x}{15} > 1.5 + 9$

Step 4.2

Add $1.5$ and $9$ .

$\frac{7 x}{15} > 10.5$

Step 5

Multiply both sides by $15$ .

$\frac{7 x}{15} \cdot 15 > 10.5 \cdot 15$

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 $15$ .

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Step 6.1.1.1

Cancel the common factor.

$\frac{7 x}{15} \cdot 15 > 10.5 \cdot 15$

Step 6.1.1.2

Rewrite the expression.

$7 x > 10.5 \cdot 15$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $10.5$ by $15$ .

$7 x > 157.5$

Step 7

Divide each term in $7 x > 157.5$ by $7$ and simplify.

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Step 7.1

Divide each term in $7 x > 157.5$ by $7$ .

$\frac{7 x}{7} > \frac{157.5}{7}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $7$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{7 x}{7} > \frac{157.5}{7}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x > \frac{157.5}{7}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $157.5$ by $7$ .

$x > 22.5$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$x > 22.5$

Interval Notation:

$(22.5, \infty)$