Solve 1/4+(1/16+1/12)x=5/6

$$\frac { 1 } { 4 } + ( \frac { 1 } { 16 } + \frac { 1 } { 12 } ) x = \frac { 5 } { 6 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Least common multiple of 16 and 12 is 48. Convert \frac{1}{16} and \frac{1}{12} to fractions with denominator 48.

$$\frac{1}{4}+\left(\frac{3}{48}+\frac{4}{48}\right)x=\frac{5}{6}$$

Since \frac{3}{48} and \frac{4}{48} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}+\frac{3+4}{48}x=\frac{5}{6}$$

Add 3 and 4 to get 7.

$$\frac{1}{4}+\frac{7}{48}x=\frac{5}{6}$$

Subtract \frac{1}{4} from both sides.

$$\frac{7}{48}x=\frac{5}{6}-\frac{1}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{7}{48}x=\frac{10}{12}-\frac{3}{12}$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{48}x=\frac{10-3}{12}$$

Subtract 3 from 10 to get 7.

$$\frac{7}{48}x=\frac{7}{12}$$

Multiply both sides by \frac{48}{7}, the reciprocal of \frac{7}{48}.

$$x=\frac{7}{12}\times \frac{48}{7}$$

Multiply \frac{7}{12} times \frac{48}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\times 48}{12\times 7}$$

Cancel out 7 in both numerator and denominator.

$$x=\frac{48}{12}$$

Divide 48 by 12 to get 4.

$$x=4$$