Solve 1/5x+2=-1/4x+3/4

$$\frac{ 1 }{ 5 } x+2 = - \frac{ 1 }{ 4 } x+ \frac{ 3 }{ 4 }$$

Solve for x

$$x = -\frac{25}{9} = -2\frac{7}{9} \approx -2.777777778$$

Steps for Solving Linear Equation

Add \frac{1}{4}x to both sides.

$$\frac{1}{5}x+2+\frac{1}{4}x=\frac{3}{4}$$

Combine \frac{1}{5}x and \frac{1}{4}x to get \frac{9}{20}x.

$$\frac{9}{20}x+2=\frac{3}{4}$$

Subtract 2 from both sides.

$$\frac{9}{20}x=\frac{3}{4}-2$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{9}{20}x=\frac{3}{4}-\frac{8}{4}$$

Since \frac{3}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{20}x=\frac{3-8}{4}$$

Subtract 8 from 3 to get -5.

$$\frac{9}{20}x=-\frac{5}{4}$$

Multiply both sides by \frac{20}{9}, the reciprocal of \frac{9}{20}.

$$x=-\frac{5}{4}\times \frac{20}{9}$$

Multiply -\frac{5}{4} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\times 20}{4\times 9}$$

Do the multiplications in the fraction \frac{-5\times 20}{4\times 9}.

$$x=\frac{-100}{36}$$

Reduce the fraction \frac{-100}{36} to lowest terms by extracting and canceling out 4.

$$x=-\frac{25}{9}$$