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

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

Solve for x

$$x = \frac{48}{7} = 6\frac{6}{7} \approx 6.857142857$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Combine \frac{2}{3}x and \frac{2}{3}x to get \frac{4}{3}x.

$$\frac{4}{3}x-\frac{2}{3}+\frac{2}{3}=\frac{5}{2}\left(x-2\right)-3$$

Add -\frac{2}{3} and \frac{2}{3} to get 0.

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

Use the distributive property to multiply \frac{5}{2} by x-2.

$$\frac{4}{3}x=\frac{5}{2}x+\frac{5}{2}\left(-2\right)-3$$

Express \frac{5}{2}\left(-2\right) as a single fraction.

$$\frac{4}{3}x=\frac{5}{2}x+\frac{5\left(-2\right)}{2}-3$$

Multiply 5 and -2 to get -10.

$$\frac{4}{3}x=\frac{5}{2}x+\frac{-10}{2}-3$$

Divide -10 by 2 to get -5.

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

Subtract 3 from -5 to get -8.

$$\frac{4}{3}x=\frac{5}{2}x-8$$

Subtract \frac{5}{2}x from both sides.

$$\frac{4}{3}x-\frac{5}{2}x=-8$$

Combine \frac{4}{3}x and -\frac{5}{2}x to get -\frac{7}{6}x.

$$-\frac{7}{6}x=-8$$

Multiply both sides by -\frac{6}{7}, the reciprocal of -\frac{7}{6}.

$$x=-8\left(-\frac{6}{7}\right)$$

Express -8\left(-\frac{6}{7}\right) as a single fraction.

$$x=\frac{-8\left(-6\right)}{7}$$

Multiply -8 and -6 to get 48.

$$x=\frac{48}{7}$$