Solve for a 21=-5/6a+1

$21 = - \frac{5}{6} a + 1$

Step 1

Rewrite the equation as $- \frac{5}{6} a + 1 = 21$ .

$- \frac{5}{6} a + 1 = 21$

Step 2

Simplify each term.

Combine $a$ and $\frac{5}{6}$ .

$- \frac{a \cdot 5}{6} + 1 = 21$

Move $5$ to the left of $a$ .

$- \frac{5 a}{6} + 1 = 21$

Step 3

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

Subtract $1$ from both sides of the equation.

$- \frac{5 a}{6} = 21 - 1$

Subtract $1$ from $21$ .

$- \frac{5 a}{6} = 20$

Step 4

Multiply both sides of the equation by $- \frac{6}{5}$ .

$- \frac{6}{5} (- \frac{5 a}{6}) = - \frac{6}{5} \cdot 20$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{5} (- \frac{5 a}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{- 6}{5} (- \frac{5 a}{6}) = - \frac{6}{5} \cdot 20$

Move the leading negative in $- \frac{5 a}{6}$ into the numerator.

$\frac{- 6}{5} \cdot \frac{- 5 a}{6} = - \frac{6}{5} \cdot 20$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{5} \cdot \frac{- 5 a}{6} = - \frac{6}{5} \cdot 20$

Cancel the common factor.

$\frac{6 \cdot - 1}{5} \cdot \frac{- 5 a}{6} = - \frac{6}{5} \cdot 20$

Rewrite the expression.

$\frac{- 1}{5} (- 5 a) = - \frac{6}{5} \cdot 20$

Cancel the common factor of $5$ .

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

$\frac{- 1}{5} (5 (- a)) = - \frac{6}{5} \cdot 20$

Cancel the common factor.

$\frac{- 1}{5} (5 (- a)) = - \frac{6}{5} \cdot 20$

Rewrite the expression.

$- - a = - \frac{6}{5} \cdot 20$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 a = - \frac{6}{5} \cdot 20$

Multiply $a$ by $1$ .

$a = - \frac{6}{5} \cdot 20$

Simplify the right side.

Simplify $- \frac{6}{5} \cdot 20$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$a = \frac{- 6}{5} \cdot 20$

Factor $5$ out of $20$ .

$a = \frac{- 6}{5} \cdot (5 (4))$

Cancel the common factor.

$a = \frac{- 6}{5} \cdot (5 \cdot 4)$

Rewrite the expression.

$a = - 6 \cdot 4$

Multiply $- 6$ by $4$ .

$a = - 24$

Solve for a 21=-5/6a+1

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