Solve 2x+7/16=3/4-1/8x-1/2

$$2 x + \frac { 7 } { 16 } = \frac { 3 } { 4 } - \frac { 1 } { 8 } x - \frac { 1 } { 2 }$$

Solve for x

$$x=-\frac{3}{34}\approx -0.088235294$$

Steps for Solving Linear Equation

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$2x+\frac{7}{16}=\frac{3}{4}-\frac{1}{8}x-\frac{2}{4}$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$2x+\frac{7}{16}=\frac{3-2}{4}-\frac{1}{8}x$$

Subtract 2 from 3 to get 1.

$$2x+\frac{7}{16}=\frac{1}{4}-\frac{1}{8}x$$

Add \frac{1}{8}x to both sides.

$$2x+\frac{7}{16}+\frac{1}{8}x=\frac{1}{4}$$

Combine 2x and \frac{1}{8}x to get \frac{17}{8}x.

$$\frac{17}{8}x+\frac{7}{16}=\frac{1}{4}$$

Subtract \frac{7}{16} from both sides.

$$\frac{17}{8}x=\frac{1}{4}-\frac{7}{16}$$

Least common multiple of 4 and 16 is 16. Convert \frac{1}{4} and \frac{7}{16} to fractions with denominator 16.

$$\frac{17}{8}x=\frac{4}{16}-\frac{7}{16}$$

Since \frac{4}{16} and \frac{7}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{8}x=\frac{4-7}{16}$$

Subtract 7 from 4 to get -3.

$$\frac{17}{8}x=-\frac{3}{16}$$

Multiply both sides by \frac{8}{17}, the reciprocal of \frac{17}{8}.

$$x=-\frac{3}{16}\times \frac{8}{17}$$

Multiply -\frac{3}{16} times \frac{8}{17} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-3\times 8}{16\times 17}$$

Do the multiplications in the fraction \frac{-3\times 8}{16\times 17}.

$$x=\frac{-24}{272}$$

Reduce the fraction \frac{-24}{272} to lowest terms by extracting and canceling out 8.

$$x=-\frac{3}{34}$$