Solve for b a=1/5(b+c-d)

$a = \frac{1}{5} (b + c - d)$

Step 1

Rewrite the equation as $\frac{1}{5} \cdot (b + c - d) = a$ .

$\frac{1}{5} \cdot (b + c - d) = a$

Step 2

Multiply both sides of the equation by $5$ .

$5 (\frac{1}{5} \cdot (b + c - d)) = 5 a$

Step 3

Simplify the left side.

Simplify $5 (\frac{1}{5} \cdot (b + c - d))$ .

Apply the distributive property.

$5 (\frac{1}{5} b + \frac{1}{5} c + \frac{1}{5} (- d)) = 5 a$

Simplify.

Combine $\frac{1}{5}$ and $b$ .

$5 (\frac{b}{5} + \frac{1}{5} c + \frac{1}{5} (- d)) = 5 a$

Combine $\frac{1}{5}$ and $c$ .

$5 (\frac{b}{5} + \frac{c}{5} + \frac{1}{5} (- d)) = 5 a$

Combine $\frac{1}{5}$ and $d$ .

$5 (\frac{b}{5} + \frac{c}{5} - \frac{d}{5}) = 5 a$

Apply the distributive property.

$5 \frac{b}{5} + 5 \frac{c}{5} + 5 (- \frac{d}{5}) = 5 a$

Simplify.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{b}{5} + 5 \frac{c}{5} + 5 (- \frac{d}{5}) = 5 a$

Rewrite the expression.

$b + 5 \frac{c}{5} + 5 (- \frac{d}{5}) = 5 a$

Cancel the common factor of $5$ .

Cancel the common factor.

$b + 5 \frac{c}{5} + 5 (- \frac{d}{5}) = 5 a$

Rewrite the expression.

$b + c + 5 (- \frac{d}{5}) = 5 a$

Cancel the common factor of $5$ .

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

$b + c + 5 \frac{- d}{5} = 5 a$

Cancel the common factor.

$b + c + 5 \frac{- d}{5} = 5 a$

Rewrite the expression.

$b + c - d = 5 a$

Step 4

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

Subtract $c$ from both sides of the equation.

$b - d = 5 a - c$

Add $d$ to both sides of the equation.

$b = 5 a - c + d$