Solve for a -8(a/8-2)=26

$- 8 (\frac{a}{8} - 2) = 26$

Step 1

Simplify.

Apply the distributive property.

$- 8 \frac{a}{8} - 8 \cdot - 2 = 26$

Cancel the common factor of $8$ .

Factor $8$ out of $- 8$ .

$8 (- 1) \frac{a}{8} - 8 \cdot - 2 = 26$

Cancel the common factor.

$8 \cdot - 1 \frac{a}{8} - 8 \cdot - 2 = 26$

Rewrite the expression.

$- 1 a - 8 \cdot - 2 = 26$

Multiply $- 8$ by $- 2$ .

$- 1 a + 16 = 26$

Rewrite $- 1 a$ as $- a$ .

$- a + 16 = 26$

Step 2

Divide each term in $(- a + 16) = 26$ by $- 8$ and simplify.

Divide each term in $(- a + 16) = 26$ by $- 8$ .

$\frac{(- a + 16)}{- 8} = \frac{26}{- 8}$

Simplify the left side.

Move the negative in front of the fraction.

$- \frac{- a + 16}{8} = \frac{26}{- 8}$

Factor $- 1$ out of $- a$ .

$- \frac{- (a) + 16}{8} = \frac{26}{- 8}$

Rewrite $16$ as $- 1 (- 16)$ .

$- \frac{- (a) - 1 (- 16)}{8} = \frac{26}{- 8}$

Factor $- 1$ out of $- (a) - 1 (- 16)$ .

$- \frac{- (a - 16)}{8} = \frac{26}{- 8}$

Simplify the expression.

Rewrite $- (a - 16)$ as $- 1 (a - 16)$ .

$- \frac{- 1 (a - 16)}{8} = \frac{26}{- 8}$

Move the negative in front of the fraction.

$- - \frac{a - 16}{8} = \frac{26}{- 8}$

Multiply $- 1$ by $- 1$ .

$1 \frac{a - 16}{8} = \frac{26}{- 8}$

Multiply $\frac{a - 16}{8}$ by $1$ .

$\frac{a - 16}{8} = \frac{26}{- 8}$

Simplify the right side.

Cancel the common factor of $26$ and $- 8$ .

Factor $2$ out of $26$ .

$\frac{a - 16}{8} = \frac{2 (13)}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

$\frac{a - 16}{8} = \frac{2 \cdot 13}{2 \cdot - 4}$

Cancel the common factor.

$\frac{a - 16}{8} = \frac{2 \cdot 13}{2 \cdot - 4}$

Rewrite the expression.

$\frac{a - 16}{8} = \frac{13}{- 4}$

Move the negative in front of the fraction.

$\frac{a - 16}{8} = - \frac{13}{4}$

Step 3

Multiply both sides of the equation by $8$ .

$8 \frac{a - 16}{8} = 8 (- \frac{13}{4})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$8 \frac{a - 16}{8} = 8 (- \frac{13}{4})$

Rewrite the expression.

$a - 16 = 8 (- \frac{13}{4})$

Simplify the right side.

Simplify $8 (- \frac{13}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{13}{4}$ into the numerator.

$a - 16 = 8 (\frac{- 13}{4})$

Factor $4$ out of $8$ .

$a - 16 = 4 (2) \frac{- 13}{4}$

Cancel the common factor.

$a - 16 = 4 \cdot 2 \frac{- 13}{4}$

Rewrite the expression.

$a - 16 = 2 \cdot - 13$

Multiply $2$ by $- 13$ .

$a - 16 = - 26$

Step 5

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

Add $16$ to both sides of the equation.

$a = - 26 + 16$

Add $- 26$ and $16$ .

$a = - 10$

Solve for a -8(a/8-2)=26

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