Solve 1-x/3<1/2

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

Solve for x

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

Solution Steps

Multiply both sides by 3. Since 3 is positive, the inequality direction remains the same.

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

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

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

Subtract 1 from both sides.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{3}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

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

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

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

Express \frac{\frac{1}{2}}{-1} as a single fraction.

$$x>\frac{1}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

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

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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