Solve 2x-3=1/3(7x+2)

$$2x-3= \frac{ 1 }{ 3 } (7x+2)$$

Solve for x

$$x=-11$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 7x+2.

$$2x-3=\frac{1}{3}\times 7x+\frac{1}{3}\times 2$$

Multiply \frac{1}{3} and 7 to get \frac{7}{3}.

$$2x-3=\frac{7}{3}x+\frac{1}{3}\times 2$$

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

$$2x-3=\frac{7}{3}x+\frac{2}{3}$$

Subtract \frac{7}{3}x from both sides.

$$2x-3-\frac{7}{3}x=\frac{2}{3}$$

Combine 2x and -\frac{7}{3}x to get -\frac{1}{3}x.

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

Add 3 to both sides.

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

Convert 3 to fraction \frac{9}{3}.

$$-\frac{1}{3}x=\frac{2}{3}+\frac{9}{3}$$

Since \frac{2}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

$$-\frac{1}{3}x=\frac{2+9}{3}$$

Add 2 and 9 to get 11.

$$-\frac{1}{3}x=\frac{11}{3}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=\frac{11}{3}\left(-3\right)$$

Express \frac{11}{3}\left(-3\right) as a single fraction.

$$x=\frac{11\left(-3\right)}{3}$$

Multiply 11 and -3 to get -33.

$$x=\frac{-33}{3}$$

Divide -33 by 3 to get -11.

$$x=-11$$