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

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

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Combine \frac{7}{8}x and \frac{3}{4}x to get \frac{13}{8}x.

$$\frac{13}{8}x-\frac{1}{16}=\frac{1}{4}+x$$

Subtract x from both sides.

$$\frac{13}{8}x-\frac{1}{16}-x=\frac{1}{4}$$

Combine \frac{13}{8}x and -x to get \frac{5}{8}x.

$$\frac{5}{8}x-\frac{1}{16}=\frac{1}{4}$$

Add \frac{1}{16} to both sides.

$$\frac{5}{8}x=\frac{1}{4}+\frac{1}{16}$$

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

$$\frac{5}{8}x=\frac{4}{16}+\frac{1}{16}$$

Since \frac{4}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{5}{8}x=\frac{4+1}{16}$$

Add 4 and 1 to get 5.

$$\frac{5}{8}x=\frac{5}{16}$$

Multiply both sides by \frac{8}{5}, the reciprocal of \frac{5}{8}.

$$x=\frac{5}{16}\times \frac{8}{5}$$

Multiply \frac{5}{16} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 8}{16\times 5}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{8}{16}$$

Reduce the fraction \frac{8}{16} to lowest terms by extracting and canceling out 8.

$$x=\frac{1}{2}$$