Solve for a 4/5a-8=a+2

$\frac{4}{5} a - 8 = a + 2$

Step 1

Combine $\frac{4}{5}$ and $a$ .

$\frac{4 a}{5} - 8 = a + 2$

Step 2

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

Subtract $a$ from both sides of the equation.

$\frac{4 a}{5} - 8 - a = 2$

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

$\frac{4 a}{5} - a \cdot \frac{5}{5} - 8 = 2$

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

$\frac{4 a}{5} + \frac{- a \cdot 5}{5} - 8 = 2$

Combine the numerators over the common denominator.

$\frac{4 a - a \cdot 5}{5} - 8 = 2$

Simplify each term.

Simplify the numerator.

Factor $a$ out of $4 a - a \cdot 5$ .

Factor $a$ out of $4 a$ .

$\frac{a \cdot 4 - a \cdot 5}{5} - 8 = 2$

Factor $a$ out of $- a \cdot 5$ .

$\frac{a \cdot 4 + a (- 1 \cdot 5)}{5} - 8 = 2$

Factor $a$ out of $a \cdot 4 + a (- 1 \cdot 5)$ .

$\frac{a (4 - 1 \cdot 5)}{5} - 8 = 2$

Multiply $- 1$ by $5$ .

$\frac{a (4 - 5)}{5} - 8 = 2$

Subtract $5$ from $4$ .

$\frac{a \cdot - 1}{5} - 8 = 2$

Move $- 1$ to the left of $a$ .

$\frac{- 1 \cdot a}{5} - 8 = 2$

Move the negative in front of the fraction.

$- \frac{a}{5} - 8 = 2$

Step 3

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

Add $8$ to both sides of the equation.

$- \frac{a}{5} = 2 + 8$

Add $2$ and $8$ .

$- \frac{a}{5} = 10$

Step 4

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{a}{5}) = - 5 \cdot 10$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 5 (- \frac{a}{5})$ .

Cancel the common factor of $5$ .

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

$- 5 \frac{- a}{5} = - 5 \cdot 10$

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- a}{5} = - 5 \cdot 10$

Cancel the common factor.

$5 \cdot - 1 \frac{- a}{5} = - 5 \cdot 10$

Rewrite the expression.

$- - a = - 5 \cdot 10$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 a = - 5 \cdot 10$

Multiply $a$ by $1$ .

$a = - 5 \cdot 10$

Simplify the right side.

Multiply $- 5$ by $10$ .

$a = - 50$

Solve for a 4/5a-8=a+2

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