Solve for a -7+3/5a=3/10a-4

$- 7 + \frac{3}{5} a = \frac{3}{10} a - 4$

Step 1

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

$- 7 + \frac{3 a}{5} = \frac{3}{10} a - 4$

Step 2

Combine $\frac{3}{10}$ and $a$ .

$- 7 + \frac{3 a}{5} = \frac{3 a}{10} - 4$

Step 3

Move all terms containing $a$ to the left side of the equation.

Subtract $\frac{3 a}{10}$ from both sides of the equation.

$- 7 + \frac{3 a}{5} - \frac{3 a}{10} = - 4$

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

$- 7 + \frac{3 a}{5} \cdot \frac{2}{2} - \frac{3 a}{10} = - 4$

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

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

$- 7 + \frac{3 a \cdot 2}{5 \cdot 2} - \frac{3 a}{10} = - 4$

Multiply $5$ by $2$ .

$- 7 + \frac{3 a \cdot 2}{10} - \frac{3 a}{10} = - 4$

Combine the numerators over the common denominator.

$- 7 + \frac{3 a \cdot 2 - 3 a}{10} = - 4$

Simplify the numerator.

Factor $3 a$ out of $3 a \cdot 2 - 3 a$ .

Factor $3 a$ out of $3 a \cdot 2$ .

$- 7 + \frac{3 a (2) - 3 a}{10} = - 4$

Factor $3 a$ out of $- 3 a$ .

$- 7 + \frac{3 a (2) + 3 a (- 1)}{10} = - 4$

Factor $3 a$ out of $3 a (2) + 3 a (- 1)$ .

$- 7 + \frac{3 a (2 - 1)}{10} = - 4$

Subtract $1$ from $2$ .

$- 7 + \frac{3 a \cdot 1}{10} = - 4$

Multiply $3$ by $1$ .

$- 7 + \frac{3 a}{10} = - 4$

Step 4

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

Add $7$ to both sides of the equation.

$\frac{3 a}{10} = - 4 + 7$

Add $- 4$ and $7$ .

$\frac{3 a}{10} = 3$

Step 5

Multiply both sides of the equation by $\frac{10}{3}$ .

$\frac{10}{3} \cdot \frac{3 a}{10} = \frac{10}{3} \cdot 3$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{10}{3} \cdot \frac{3 a}{10}$ .

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10}{3} \cdot \frac{3 a}{10} = \frac{10}{3} \cdot 3$

Rewrite the expression.

$\frac{1}{3} (3 a) = \frac{10}{3} \cdot 3$

Cancel the common factor of $3$ .

Factor $3$ out of $3 a$ .

$\frac{1}{3} (3 (a)) = \frac{10}{3} \cdot 3$

Cancel the common factor.

$\frac{1}{3} (3 a) = \frac{10}{3} \cdot 3$

Rewrite the expression.

$a = \frac{10}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$a = \frac{10}{3} \cdot 3$

Rewrite the expression.

$a = 10$

Solve for a -7+3/5a=3/10a-4

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