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

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

Solve for x

$$x = \frac{49}{6} = 8\frac{1}{6} \approx 8.166666667$$

Steps for Solving Linear Equation

Convert 5 to fraction \frac{15}{3}.

$$\frac{15}{3}-\frac{1}{2}x+\frac{1}{3}=\frac{5}{4}$$

Since \frac{15}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{15+1}{3}-\frac{1}{2}x=\frac{5}{4}$$

Add 15 and 1 to get 16.

$$\frac{16}{3}-\frac{1}{2}x=\frac{5}{4}$$

Subtract \frac{16}{3} from both sides.

$$-\frac{1}{2}x=\frac{5}{4}-\frac{16}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{16}{3} to fractions with denominator 12.

$$-\frac{1}{2}x=\frac{15}{12}-\frac{64}{12}$$

Since \frac{15}{12} and \frac{64}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}x=\frac{15-64}{12}$$

Subtract 64 from 15 to get -49.

$$-\frac{1}{2}x=-\frac{49}{12}$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$x=-\frac{49}{12}\left(-2\right)$$

Express -\frac{49}{12}\left(-2\right) as a single fraction.

$$x=\frac{-49\left(-2\right)}{12}$$

Multiply -49 and -2 to get 98.

$$x=\frac{98}{12}$$

Reduce the fraction \frac{98}{12} to lowest terms by extracting and canceling out 2.

$$x=\frac{49}{6}$$