Algebra Examples

$\frac{7}{10} > \frac{4}{5} + g$

Step 1

Rewrite so $g$ is on the left side of the inequality.

$\frac{4}{5} + g < \frac{7}{10}$

Step 2

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

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Step 2.1

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

$g < \frac{7}{10} - \frac{4}{5}$

Step 2.2

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$g < \frac{7}{10} - \frac{4}{5} \cdot \frac{2}{2}$

Step 2.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

$g < \frac{7}{10} - \frac{4 \cdot 2}{5 \cdot 2}$

Step 2.3.2

Multiply $5$ by $2$ .

$g < \frac{7}{10} - \frac{4 \cdot 2}{10}$

Step 2.4

Combine the numerators over the common denominator.

$g < \frac{7 - 4 \cdot 2}{10}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 4$ by $2$ .

$g < \frac{7 - 8}{10}$

Step 2.5.2

Subtract $8$ from $7$ .

$g < \frac{- 1}{10}$

Step 2.6

Move the negative in front of the fraction.

$g < - \frac{1}{10}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$g < - \frac{1}{10}$

Interval Notation:

$(- \infty, - \frac{1}{10})$