Solve a/b-3=1/2

$$\frac { a } { b } - 3 = \frac { 1 } { 2 }$$

Solve for a

$$a=\frac{7b}{2}$$

$$b\neq 0$$

Steps for Solving Linear Equation

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

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

Multiply 2 and -3 to get -6.

$$2a-6b=b$$

Add 6b to both sides.

$$2a=b+6b$$

Combine b and 6b to get 7b.

$$2a=7b$$

Divide both sides by 2.

$$\frac{2a}{2}=\frac{7b}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{7b}{2}$$

Solve for b

$$b=\frac{2a}{7}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2b, the least common multiple of b,2.

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

Multiply 2 and -3 to get -6.

$$2a-6b=b$$

Subtract b from both sides.

$$2a-6b-b=0$$

Combine -6b and -b to get -7b.

$$2a-7b=0$$

Subtract 2a from both sides. Anything subtracted from zero gives its negation.

$$-7b=-2a$$

Divide both sides by -7.

$$\frac{-7b}{-7}=-\frac{2a}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$b=-\frac{2a}{-7}$$

Divide -2a by -7.

$$b=\frac{2a}{7}$$

Variable b cannot be equal to 0.

$$b=\frac{2a}{7}\text{, }b\neq 0$$