Solve for g 2/5(g-7)=3

$\frac{2}{5} (g - 7) = 3$

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} (\frac{2}{5} \cdot (g - 7)) = \frac{5}{2} \cdot 3$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{2} (\frac{2}{5} \cdot (g - 7))$ .

Apply the distributive property.

$\frac{5}{2} (\frac{2}{5} g + \frac{2}{5} \cdot - 7) = \frac{5}{2} \cdot 3$

Combine $\frac{2}{5}$ and $g$ .

$\frac{5}{2} (\frac{2 g}{5} + \frac{2}{5} \cdot - 7) = \frac{5}{2} \cdot 3$

Multiply $\frac{2}{5} \cdot - 7$ .

Combine $\frac{2}{5}$ and $- 7$ .

$\frac{5}{2} (\frac{2 g}{5} + \frac{2 \cdot - 7}{5}) = \frac{5}{2} \cdot 3$

Multiply $2$ by $- 7$ .

$\frac{5}{2} (\frac{2 g}{5} + \frac{- 14}{5}) = \frac{5}{2} \cdot 3$

Move the negative in front of the fraction.

$\frac{5}{2} (\frac{2 g}{5} - \frac{14}{5}) = \frac{5}{2} \cdot 3$

Apply the distributive property.

$\frac{5}{2} \cdot \frac{2 g}{5} + \frac{5}{2} (- \frac{14}{5}) = \frac{5}{2} \cdot 3$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 g}{5} + \frac{5}{2} (- \frac{14}{5}) = \frac{5}{2} \cdot 3$

Rewrite the expression.

$\frac{1}{2} (2 g) + \frac{5}{2} (- \frac{14}{5}) = \frac{5}{2} \cdot 3$

Cancel the common factor of $2$ .

Factor $2$ out of $2 g$ .

$\frac{1}{2} (2 (g)) + \frac{5}{2} (- \frac{14}{5}) = \frac{5}{2} \cdot 3$

Cancel the common factor.

$\frac{1}{2} (2 g) + \frac{5}{2} (- \frac{14}{5}) = \frac{5}{2} \cdot 3$

Rewrite the expression.

$g + \frac{5}{2} (- \frac{14}{5}) = \frac{5}{2} \cdot 3$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{14}{5}$ into the numerator.

$g + \frac{5}{2} \cdot \frac{- 14}{5} = \frac{5}{2} \cdot 3$

Cancel the common factor.

$g + \frac{5}{2} \cdot \frac{- 14}{5} = \frac{5}{2} \cdot 3$

Rewrite the expression.

$g + \frac{1}{2} \cdot - 14 = \frac{5}{2} \cdot 3$

Cancel the common factor of $2$ .

Factor $2$ out of $- 14$ .

$g + \frac{1}{2} \cdot (2 (- 7)) = \frac{5}{2} \cdot 3$

Cancel the common factor.

$g + \frac{1}{2} \cdot (2 \cdot - 7) = \frac{5}{2} \cdot 3$

Rewrite the expression.

$g - 7 = \frac{5}{2} \cdot 3$

Simplify the right side.

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

Combine $\frac{5}{2}$ and $3$ .

$g - 7 = \frac{5 \cdot 3}{2}$

Multiply $5$ by $3$ .

$g - 7 = \frac{15}{2}$

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

Add $7$ to both sides of the equation.

$g = \frac{15}{2} + 7$

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$g = \frac{15}{2} + 7 \cdot \frac{2}{2}$

Combine $7$ and $\frac{2}{2}$ .

$g = \frac{15}{2} + \frac{7 \cdot 2}{2}$

Combine the numerators over the common denominator.

$g = \frac{15 + 7 \cdot 2}{2}$

Simplify the numerator.

Multiply $7$ by $2$ .

$g = \frac{15 + 14}{2}$

Add $15$ and $14$ .

$g = \frac{29}{2}$

The result can be shown in multiple forms.

Exact Form:

$g = \frac{29}{2}$

Decimal Form:

$g = 14.5$

Mixed Number Form:

$g = 14 \frac{1}{2}$

Solve for g 2/5(g-7)=3

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