Solve 18+30/16/frac{18+a{16}}=1/2

$$\frac { \frac { 18 + 30 } { 16 } } { \frac { 18 + a } { 16 } } = \frac { 1 } { 2 }$$

Solve for a

$$a=78$$

Steps for Solving Linear Equation

Divide \frac{18+30}{16} by \frac{18+a}{16} by multiplying \frac{18+30}{16} by the reciprocal of \frac{18+a}{16}.

$$\frac{\left(18+30\right)\times 16}{16\left(18+a\right)}=\frac{1}{2}$$

Cancel out 16 in both numerator and denominator.

$$\frac{18+30}{a+18}=\frac{1}{2}$$

Add 18 and 30 to get 48.

$$\frac{48}{a+18}=\frac{1}{2}$$

Variable a cannot be equal to -18 since division by zero is not defined. Multiply both sides of the equation by 2\left(a+18\right), the least common multiple of a+18,2.

$$2\times 48=a+18$$

Multiply 2 and 48 to get 96.

$$96=a+18$$

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

$$a+18=96$$

Subtract 18 from both sides.

$$a=96-18$$

Subtract 18 from 96 to get 78.

$$a=78$$