Solve for b a=3/4(b+c)

$a = \frac{3}{4} (b + c)$

Step 1

Rewrite the equation as $\frac{3}{4} \cdot (b + c) = a$ .

$\frac{3}{4} \cdot (b + c) = a$

Step 2

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} (\frac{3}{4} \cdot (b + c)) = \frac{4}{3} a$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} (\frac{3}{4} \cdot (b + c))$ .

Apply the distributive property.

$\frac{4}{3} (\frac{3}{4} b + \frac{3}{4} c) = \frac{4}{3} a$

Combine $\frac{3}{4}$ and $b$ .

$\frac{4}{3} (\frac{3 b}{4} + \frac{3}{4} c) = \frac{4}{3} a$

Combine $\frac{3}{4}$ and $c$ .

$\frac{4}{3} (\frac{3 b}{4} + \frac{3 c}{4}) = \frac{4}{3} a$

Apply the distributive property.

$\frac{4}{3} \cdot \frac{3 b}{4} + \frac{4}{3} \cdot \frac{3 c}{4} = \frac{4}{3} a$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 b}{4} + \frac{4}{3} \cdot \frac{3 c}{4} = \frac{4}{3} a$

Rewrite the expression.

$\frac{1}{3} (3 b) + \frac{4}{3} \cdot \frac{3 c}{4} = \frac{4}{3} a$

Cancel the common factor of $3$ .

Factor $3$ out of $3 b$ .

$\frac{1}{3} (3 (b)) + \frac{4}{3} \cdot \frac{3 c}{4} = \frac{4}{3} a$

Cancel the common factor.

$\frac{1}{3} (3 b) + \frac{4}{3} \cdot \frac{3 c}{4} = \frac{4}{3} a$

Rewrite the expression.

$b + \frac{4}{3} \cdot \frac{3 c}{4} = \frac{4}{3} a$

Cancel the common factor of $4$ .

Cancel the common factor.

$b + \frac{4}{3} \cdot \frac{3 c}{4} = \frac{4}{3} a$

Rewrite the expression.

$b + \frac{1}{3} (3 c) = \frac{4}{3} a$

Cancel the common factor of $3$ .

Factor $3$ out of $3 c$ .

$b + \frac{1}{3} (3 (c)) = \frac{4}{3} a$

Cancel the common factor.

$b + \frac{1}{3} (3 c) = \frac{4}{3} a$

Rewrite the expression.

$b + c = \frac{4}{3} a$

Simplify the right side.

Combine $\frac{4}{3}$ and $a$ .

$b + c = \frac{4 a}{3}$

Step 4

Subtract $c$ from both sides of the equation.

$b = \frac{4 a}{3} - c$

Solve for b a=3/4(b+c)

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