Solve 1/2a*(12/a-b)=2

$$\frac { 1 } { 2 } a \cdot ( \frac { 12 } { a } - b ) = 2$$

Solve for b

$$b=\frac{8}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}a\left(\frac{12}{a}-b\right)\times 2a=4a$$

To add or subtract expressions, expand them to make their denominators the same. Multiply b times \frac{a}{a}.

$$\frac{1}{2}a\left(\frac{12}{a}-\frac{ba}{a}\right)\times 2a=4a$$

Since \frac{12}{a} and \frac{ba}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}a\times \frac{12-ba}{a}\times 2a=4a$$

Multiply \frac{1}{2} and 2 to get 1.

$$a\times \frac{12-ba}{a}a=4a$$

Multiply a and a to get a^{2}.

$$a^{2}\times \frac{12-ba}{a}=4a$$

Express a^{2}\times \frac{12-ba}{a} as a single fraction.

$$\frac{a^{2}\left(12-ba\right)}{a}=4a$$

Cancel out a in both numerator and denominator.

$$a\left(-ab+12\right)=4a$$

Use the distributive property to multiply a by -ab+12.

$$-ba^{2}+12a=4a$$

Subtract 12a from both sides.

$$-ba^{2}=4a-12a$$

Combine 4a and -12a to get -8a.

$$-ba^{2}=-8a$$

The equation is in standard form.

$$\left(-a^{2}\right)b=-8a$$

Divide both sides by -a^{2}.

$$\frac{\left(-a^{2}\right)b}{-a^{2}}=-\frac{8a}{-a^{2}}$$

Dividing by -a^{2} undoes the multiplication by -a^{2}.

$$b=-\frac{8a}{-a^{2}}$$

Divide -8a by -a^{2}.

$$b=\frac{8}{a}$$

Solve for a

$$a=\frac{8}{b}$$

$$b\neq 0$$