Solve x-4/3-2/3x+1/2=2x+2

$$x - \frac { 4 } { 3 } - \frac { 2 } { 3 } x + \frac { 1 } { 2 } = 2 x + 2$$

Solve for x

$$x = -\frac{17}{10} = -1\frac{7}{10} = -1.7$$

Steps for Solving Linear Equation

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

$$\frac{1}{3}x-\frac{4}{3}+\frac{1}{2}=2x+2$$

Least common multiple of 3 and 2 is 6. Convert -\frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{1}{3}x-\frac{8}{6}+\frac{3}{6}=2x+2$$

Since -\frac{8}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}x+\frac{-8+3}{6}=2x+2$$

Add -8 and 3 to get -5.

$$\frac{1}{3}x-\frac{5}{6}=2x+2$$

Subtract 2x from both sides.

$$\frac{1}{3}x-\frac{5}{6}-2x=2$$

Combine \frac{1}{3}x and -2x to get -\frac{5}{3}x.

$$-\frac{5}{3}x-\frac{5}{6}=2$$

Add \frac{5}{6} to both sides.

$$-\frac{5}{3}x=2+\frac{5}{6}$$

Convert 2 to fraction \frac{12}{6}.

$$-\frac{5}{3}x=\frac{12}{6}+\frac{5}{6}$$

Since \frac{12}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$-\frac{5}{3}x=\frac{12+5}{6}$$

Add 12 and 5 to get 17.

$$-\frac{5}{3}x=\frac{17}{6}$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}.

$$x=\frac{17}{6}\left(-\frac{3}{5}\right)$$

Multiply \frac{17}{6} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{17\left(-3\right)}{6\times 5}$$

Do the multiplications in the fraction \frac{17\left(-3\right)}{6\times 5}.

$$x=\frac{-51}{30}$$

Reduce the fraction \frac{-51}{30} to lowest terms by extracting and canceling out 3.

$$x=-\frac{17}{10}$$