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

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

Solve for x

$$x = \frac{54}{7} = 7\frac{5}{7} \approx 7.714285714$$

Steps for Solving Linear Equation

Convert 5 to fraction \frac{10}{2}.

$$\frac{10}{2}-\frac{1}{3}x-\frac{1}{2}=\frac{1}{4}x$$

Since \frac{10}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-1}{2}-\frac{1}{3}x=\frac{1}{4}x$$

Subtract 1 from 10 to get 9.

$$\frac{9}{2}-\frac{1}{3}x=\frac{1}{4}x$$

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

$$\frac{9}{2}-\frac{1}{3}x-\frac{1}{4}x=0$$

Combine -\frac{1}{3}x and -\frac{1}{4}x to get -\frac{7}{12}x.

$$\frac{9}{2}-\frac{7}{12}x=0$$

Subtract \frac{9}{2} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{7}{12}x=-\frac{9}{2}$$

Multiply both sides by -\frac{12}{7}, the reciprocal of -\frac{7}{12}.

$$x=-\frac{9}{2}\left(-\frac{12}{7}\right)$$

Multiply -\frac{9}{2} times -\frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\left(-12\right)}{2\times 7}$$

Do the multiplications in the fraction \frac{-9\left(-12\right)}{2\times 7}.

$$x=\frac{108}{14}$$

Reduce the fraction \frac{108}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{54}{7}$$