Solve the Inequality for g 7/10>4/5+g

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

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.

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

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

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

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

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

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

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

Multiply $5$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 4$ by $2$ .

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

Subtract $8$ from $7$ .

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

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:

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