Solve a-c/2=a-4b/3

$$\frac { a - c } { 2 } = \frac { a - 4 b } { 3 }$$

Solve for a

$$a=3c-8b$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(a-c\right)=2\left(a-4b\right)$$

Use the distributive property to multiply 3 by a-c.

$$3a-3c=2\left(a-4b\right)$$

Use the distributive property to multiply 2 by a-4b.

$$3a-3c=2a-8b$$

Subtract 2a from both sides.

$$3a-3c-2a=-8b$$

Combine 3a and -2a to get a.

$$a-3c=-8b$$

Add 3c to both sides.

$$a=-8b+3c$$

Solve for b

$$b=\frac{3c-a}{8}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(a-c\right)=2\left(a-4b\right)$$

Use the distributive property to multiply 3 by a-c.

$$3a-3c=2\left(a-4b\right)$$

Use the distributive property to multiply 2 by a-4b.

$$3a-3c=2a-8b$$

Swap sides so that all variable terms are on the left hand side.

$$2a-8b=3a-3c$$

Subtract 2a from both sides.

$$-8b=3a-3c-2a$$

Combine 3a and -2a to get a.

$$-8b=a-3c$$

Divide both sides by -8.

$$\frac{-8b}{-8}=\frac{a-3c}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$b=\frac{a-3c}{-8}$$

Divide a-3c by -8.

$$b=\frac{3c-a}{8}$$