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

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

Solve for x

$$x = \frac{19}{15} = 1\frac{4}{15} \approx 1.266666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply -4 by 2-3x.

$$-8+12x=5-\left(\frac{1}{3}-2x\right)$$

To find the opposite of \frac{1}{3}-2x, find the opposite of each term.

$$-8+12x=5-\frac{1}{3}-\left(-2x\right)$$

The opposite of -2x is 2x.

$$-8+12x=5-\frac{1}{3}+2x$$

Convert 5 to fraction \frac{15}{3}.

$$-8+12x=\frac{15}{3}-\frac{1}{3}+2x$$

Since \frac{15}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$-8+12x=\frac{15-1}{3}+2x$$

Subtract 1 from 15 to get 14.

$$-8+12x=\frac{14}{3}+2x$$

Subtract 2x from both sides.

$$-8+12x-2x=\frac{14}{3}$$

Combine 12x and -2x to get 10x.

$$-8+10x=\frac{14}{3}$$

Add 8 to both sides.

$$10x=\frac{14}{3}+8$$

Convert 8 to fraction \frac{24}{3}.

$$10x=\frac{14}{3}+\frac{24}{3}$$

Since \frac{14}{3} and \frac{24}{3} have the same denominator, add them by adding their numerators.

$$10x=\frac{14+24}{3}$$

Add 14 and 24 to get 38.

$$10x=\frac{38}{3}$$

Divide both sides by 10.

$$x=\frac{\frac{38}{3}}{10}$$

Express \frac{\frac{38}{3}}{10} as a single fraction.

$$x=\frac{38}{3\times 10}$$

Multiply 3 and 10 to get 30.

$$x=\frac{38}{30}$$

Reduce the fraction \frac{38}{30} to lowest terms by extracting and canceling out 2.

$$x=\frac{19}{15}$$