Solve 1/3-1>1/2+2x

$$\frac { 1 } { 3 } - 1 > \frac { 1 } { 2 } + 2 x$$

Solve for x

$$x<-\frac{7}{12}$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{3}-\frac{3}{3}>\frac{1}{2}+2x$$

Since \frac{1}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-3}{3}>\frac{1}{2}+2x$$

Subtract 3 from 1 to get -2.

$$-\frac{2}{3}>\frac{1}{2}+2x$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$\frac{1}{2}+2x<-\frac{2}{3}$$

Subtract \frac{1}{2} from both sides.

$$2x<-\frac{2}{3}-\frac{1}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$2x<-\frac{4}{6}-\frac{3}{6}$$

Since -\frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$2x<\frac{-4-3}{6}$$

Subtract 3 from -4 to get -7.

$$2x<-\frac{7}{6}$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x<\frac{-\frac{7}{6}}{2}$$

Express \frac{-\frac{7}{6}}{2} as a single fraction.

$$x<\frac{-7}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$x<\frac{-7}{12}$$

Fraction \frac{-7}{12} can be rewritten as -\frac{7}{12} by extracting the negative sign.

$$x<-\frac{7}{12}$$