Solve 5/6x+1=1/4-1/2x

$$\frac{ 5 }{ 6 } x+1= \frac{ 1 }{ 4 } - \frac{ 1 }{ 2 } x$$

Solve for x

$$x=-\frac{9}{16}=-0.5625$$

Steps for Solving Linear Equation

Add \frac{1}{2}x to both sides.

$$\frac{5}{6}x+1+\frac{1}{2}x=\frac{1}{4}$$

Combine \frac{5}{6}x and \frac{1}{2}x to get \frac{4}{3}x.

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

Subtract 1 from both sides.

$$\frac{4}{3}x=\frac{1}{4}-1$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{4}{3}x=\frac{1}{4}-\frac{4}{4}$$

Since \frac{1}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}x=\frac{1-4}{4}$$

Subtract 4 from 1 to get -3.

$$\frac{4}{3}x=-\frac{3}{4}$$

Multiply both sides by \frac{3}{4}, the reciprocal of \frac{4}{3}.

$$x=-\frac{3}{4}\times \frac{3}{4}$$

Multiply -\frac{3}{4} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-3\times 3}{4\times 4}$$

Do the multiplications in the fraction \frac{-3\times 3}{4\times 4}.

$$x=\frac{-9}{16}$$

Fraction \frac{-9}{16} can be rewritten as -\frac{9}{16} by extracting the negative sign.

$$x=-\frac{9}{16}$$