Solve 1/3-x>4-3x

$$\frac{ 1 }{ 3 } -x > 4-3x$$

Solve for x

$$x>\frac{11}{6}$$

Solution Steps

Add 3x to both sides.

$$\frac{1}{3}-x+3x>4$$

Combine -x and 3x to get 2x.

$$\frac{1}{3}+2x>4$$

Subtract \frac{1}{3} from both sides.

$$2x>4-\frac{1}{3}$$

Convert 4 to fraction \frac{12}{3}.

$$2x>\frac{12}{3}-\frac{1}{3}$$

Since \frac{12}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$2x>\frac{12-1}{3}$$

Subtract 1 from 12 to get 11.

$$2x>\frac{11}{3}$$

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

$$x>\frac{\frac{11}{3}}{2}$$

Express \frac{\frac{11}{3}}{2} as a single fraction.

$$x>\frac{11}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x>\frac{11}{6}$$