Solve 4x-1/3<5-2(3-x)

$$4 x - \frac { 1 } { 3 } < 5 - 2 ( 3 - x )$$

Solve for x

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

Solution Steps

Use the distributive property to multiply -2 by 3-x.

$$4x-\frac{1}{3}<5-6+2x$$

Subtract 6 from 5 to get -1.

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

Subtract 2x from both sides.

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

Combine 4x and -2x to get 2x.

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

Add \frac{1}{3} to both sides.

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

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

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

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

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

Add -3 and 1 to get -2.

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

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

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

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

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

Multiply 3 and 2 to get 6.

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

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

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