Solve 1/3(2x+7/2)=3/4

$$\frac { 1 } { 3 } ( 2 x + \frac { 7 } { 2 } ) = \frac { 3 } { 4 }$$

Solve for x

$$x=-\frac{5}{8}=-0.625$$

Steps for Solving Linear Equation

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$2x+\frac{7}{2}=\frac{3}{4}\times 3$$

Express \frac{3}{4}\times 3 as a single fraction.

$$2x+\frac{7}{2}=\frac{3\times 3}{4}$$

Multiply 3 and 3 to get 9.

$$2x+\frac{7}{2}=\frac{9}{4}$$

Subtract \frac{7}{2} from both sides.

$$2x=\frac{9}{4}-\frac{7}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{7}{2} to fractions with denominator 4.

$$2x=\frac{9}{4}-\frac{14}{4}$$

Since \frac{9}{4} and \frac{14}{4} have the same denominator, subtract them by subtracting their numerators.

$$2x=\frac{9-14}{4}$$

Subtract 14 from 9 to get -5.

$$2x=-\frac{5}{4}$$

Divide both sides by 2.

$$x=\frac{-\frac{5}{4}}{2}$$

Express \frac{-\frac{5}{4}}{2} as a single fraction.

$$x=\frac{-5}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$x=\frac{-5}{8}$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$x=-\frac{5}{8}$$