Solve 5/8x-1=1/4x-1/16

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

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

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

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

Combine \frac{5}{8}x and -\frac{1}{4}x to get \frac{3}{8}x.

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

Add 1 to both sides.

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

Convert 1 to fraction \frac{16}{16}.

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

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

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

Add -1 and 16 to get 15.

$$\frac{3}{8}x=\frac{15}{16}$$

Multiply both sides by \frac{8}{3}, the reciprocal of \frac{3}{8}.

$$x=\frac{15}{16}\times \frac{8}{3}$$

Multiply \frac{15}{16} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{15\times 8}{16\times 3}$$

Do the multiplications in the fraction \frac{15\times 8}{16\times 3}.

$$x=\frac{120}{48}$$

Reduce the fraction \frac{120}{48} to lowest terms by extracting and canceling out 24.

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