Solve 3/4x+1/2x-x+8/3=27/2

$$\frac { 3 } { 4 } x + \frac { 1 } { 2 } x - x + \frac { 8 } { 3 } = \frac { 27 } { 2 }$$

Solve for x

$$x = \frac{130}{3} = 43\frac{1}{3} \approx 43.333333333$$

Steps for Solving Linear Equation

Combine \frac{3}{4}x and \frac{1}{2}x to get \frac{5}{4}x.

$$\frac{5}{4}x-x+\frac{8}{3}=\frac{27}{2}$$

Combine \frac{5}{4}x and -x to get \frac{1}{4}x.

$$\frac{1}{4}x+\frac{8}{3}=\frac{27}{2}$$

Subtract \frac{8}{3} from both sides.

$$\frac{1}{4}x=\frac{27}{2}-\frac{8}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{27}{2} and \frac{8}{3} to fractions with denominator 6.

$$\frac{1}{4}x=\frac{81}{6}-\frac{16}{6}$$

Since \frac{81}{6} and \frac{16}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}x=\frac{81-16}{6}$$

Subtract 16 from 81 to get 65.

$$\frac{1}{4}x=\frac{65}{6}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x=\frac{65}{6}\times 4$$

Express \frac{65}{6}\times 4 as a single fraction.

$$x=\frac{65\times 4}{6}$$

Multiply 65 and 4 to get 260.

$$x=\frac{260}{6}$$

Reduce the fraction \frac{260}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{130}{3}$$