Solve the Inequality for g 4g-2/5<1/3

$4 g - \frac{2}{5} < \frac{1}{3}$

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

Add $\frac{2}{5}$ to both sides of the inequality.

$4 g < \frac{1}{3} + \frac{2}{5}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$4 g < \frac{1}{3} \cdot \frac{5}{5} + \frac{2}{5}$

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 g < \frac{1}{3} \cdot \frac{5}{5} + \frac{2}{5} \cdot \frac{3}{3}$

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

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$4 g < \frac{5}{3 \cdot 5} + \frac{2}{5} \cdot \frac{3}{3}$

Multiply $3$ by $5$ .

$4 g < \frac{5}{15} + \frac{2}{5} \cdot \frac{3}{3}$

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

$4 g < \frac{5}{15} + \frac{2 \cdot 3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$4 g < \frac{5}{15} + \frac{2 \cdot 3}{15}$

Combine the numerators over the common denominator.

$4 g < \frac{5 + 2 \cdot 3}{15}$

Simplify the numerator.

Multiply $2$ by $3$ .

$4 g < \frac{5 + 6}{15}$

Add $5$ and $6$ .

$4 g < \frac{11}{15}$

Divide each term in $4 g < \frac{11}{15}$ by $4$ and simplify.

Divide each term in $4 g < \frac{11}{15}$ by $4$ .

$\frac{4 g}{4} < \frac{\frac{11}{15}}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 g}{4} < \frac{\frac{11}{15}}{4}$

Divide $g$ by $1$ .

$g < \frac{\frac{11}{15}}{4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$g < \frac{11}{15} \cdot \frac{1}{4}$

Multiply $\frac{11}{15} \cdot \frac{1}{4}$ .

Multiply $\frac{11}{15}$ by $\frac{1}{4}$ .

$g < \frac{11}{15 \cdot 4}$

Multiply $15$ by $4$ .

$g < \frac{11}{60}$

The result can be shown in multiple forms.

Inequality Form:

$g < \frac{11}{60}$

Interval Notation:

$(- \infty, \frac{11}{60})$

Solve the Inequality for g 4g-2/5<1/3

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