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

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

Evaluate

$$\frac{5\left(x-2\right)}{3}$$

Solution Steps

Use the distributive property to multiply -\frac{2}{3} by 2x-1.

$$3x-\frac{2}{3}\times 2x-\frac{2}{3}\left(-1\right)-4$$

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

$$3x+\frac{-2\times 2}{3}x-\frac{2}{3}\left(-1\right)-4$$

Multiply -2 and 2 to get -4.

$$3x+\frac{-4}{3}x-\frac{2}{3}\left(-1\right)-4$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$3x-\frac{4}{3}x-\frac{2}{3}\left(-1\right)-4$$

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

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

Combine 3x and -\frac{4}{3}x to get \frac{5}{3}x.

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

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

$$\frac{5}{3}x+\frac{2}{3}-\frac{12}{3}$$

Since \frac{2}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}x+\frac{2-12}{3}$$

Subtract 12 from 2 to get -10.

$$\frac{5}{3}x-\frac{10}{3}$$

Expand

$$\frac{5x-10}{3}$$

Solution Steps

Use the distributive property to multiply -\frac{2}{3} by 2x-1.

$$3x-\frac{2}{3}\times 2x-\frac{2}{3}\left(-1\right)-4$$

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

$$3x+\frac{-2\times 2}{3}x-\frac{2}{3}\left(-1\right)-4$$

Multiply -2 and 2 to get -4.

$$3x+\frac{-4}{3}x-\frac{2}{3}\left(-1\right)-4$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$3x-\frac{4}{3}x-\frac{2}{3}\left(-1\right)-4$$

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

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

Combine 3x and -\frac{4}{3}x to get \frac{5}{3}x.

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

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

$$\frac{5}{3}x+\frac{2}{3}-\frac{12}{3}$$

Since \frac{2}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}x+\frac{2-12}{3}$$

Subtract 12 from 2 to get -10.

$$\frac{5}{3}x-\frac{10}{3}$$