Solve 1c+b(5/2-3/2c)=5

$$1 c + b ( \frac { 5 } { 2 } - \frac { 3 } { 2 } c ) = 5$$

Solve for b

$$b=-\frac{2\left(c-5\right)}{5-3c}$$

$$c\neq \frac{5}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply b by \frac{5}{2}-\frac{3}{2}c.

$$1c+\frac{5}{2}b-\frac{3}{2}bc=5$$

Subtract 1c from both sides.

$$\frac{5}{2}b-\frac{3}{2}bc=5-c$$

Combine all terms containing b.

$$\left(\frac{5}{2}-\frac{3}{2}c\right)b=5-c$$

The equation is in standard form.

$$\frac{5-3c}{2}b=5-c$$

Divide both sides by \frac{5}{2}-\frac{3}{2}c.

$$\frac{2\times \frac{5-3c}{2}b}{5-3c}=\frac{2\left(5-c\right)}{5-3c}$$

Dividing by \frac{5}{2}-\frac{3}{2}c undoes the multiplication by \frac{5}{2}-\frac{3}{2}c.

$$b=\frac{2\left(5-c\right)}{5-3c}$$

Solve for c

$$c=-\frac{5\left(b-2\right)}{2-3b}$$

$$b\neq \frac{2}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply b by \frac{5}{2}-\frac{3}{2}c.

$$1c+\frac{5}{2}b-\frac{3}{2}bc=5$$

Subtract \frac{5}{2}b from both sides.

$$1c-\frac{3}{2}bc=5-\frac{5}{2}b$$

Reorder the terms.

$$-\frac{3}{2}bc+c=-\frac{5}{2}b+5$$

Combine all terms containing c.

$$\left(-\frac{3}{2}b+1\right)c=-\frac{5}{2}b+5$$

The equation is in standard form.

$$\left(-\frac{3b}{2}+1\right)c=-\frac{5b}{2}+5$$

Divide both sides by 1-\frac{3}{2}b.

$$\frac{\left(-\frac{3b}{2}+1\right)c}{-\frac{3b}{2}+1}=\frac{-\frac{5b}{2}+5}{-\frac{3b}{2}+1}$$

Dividing by 1-\frac{3}{2}b undoes the multiplication by 1-\frac{3}{2}b.

$$c=\frac{-\frac{5b}{2}+5}{-\frac{3b}{2}+1}$$

Divide -\frac{5b}{2}+5 by 1-\frac{3}{2}b.

$$c=\frac{5\left(2-b\right)}{2-3b}$$