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

$$2 x / 3 - 1 / 2 = 1 / 3 ( x - 7 / 3 )$$

Solve for x

$$x=-\frac{5}{6}\approx -0.833333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\times 2x-3=2\left(x-\frac{7}{3}\right)$$

Multiply 2 and 2 to get 4.

$$4x-3=2\left(x-\frac{7}{3}\right)$$

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

$$4x-3=2x+2\left(-\frac{7}{3}\right)$$

Express 2\left(-\frac{7}{3}\right) as a single fraction.

$$4x-3=2x+\frac{2\left(-7\right)}{3}$$

Multiply 2 and -7 to get -14.

$$4x-3=2x+\frac{-14}{3}$$

Fraction \frac{-14}{3} can be rewritten as -\frac{14}{3} by extracting the negative sign.

$$4x-3=2x-\frac{14}{3}$$

Subtract 2x from both sides.

$$4x-3-2x=-\frac{14}{3}$$

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

$$2x-3=-\frac{14}{3}$$

Add 3 to both sides.

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

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

$$2x=-\frac{14}{3}+\frac{9}{3}$$

Since -\frac{14}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

$$2x=\frac{-14+9}{3}$$

Add -14 and 9 to get -5.

$$2x=-\frac{5}{3}$$

Divide both sides by 2.

$$x=\frac{-\frac{5}{3}}{2}$$

Express \frac{-\frac{5}{3}}{2} as a single fraction.

$$x=\frac{-5}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x=\frac{-5}{6}$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$x=-\frac{5}{6}$$