Solve 1/2x+1/4=1(5/6x+5)

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

Solve for x

$$x = -\frac{57}{4} = -14\frac{1}{4} = -14.25$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1 by \frac{5}{6}x+5.

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

Subtract \frac{5}{6}x from both sides.

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

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

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

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

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

Convert 5 to fraction \frac{20}{4}.

$$-\frac{1}{3}x=\frac{20}{4}-\frac{1}{4}$$

Since \frac{20}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}x=\frac{20-1}{4}$$

Subtract 1 from 20 to get 19.

$$-\frac{1}{3}x=\frac{19}{4}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=\frac{19}{4}\left(-3\right)$$

Express \frac{19}{4}\left(-3\right) as a single fraction.

$$x=\frac{19\left(-3\right)}{4}$$

Multiply 19 and -3 to get -57.

$$x=\frac{-57}{4}$$

Fraction \frac{-57}{4} can be rewritten as -\frac{57}{4} by extracting the negative sign.

$$x=-\frac{57}{4}$$