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

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

Solve for x

$$x = \frac{79}{29} = 2\frac{21}{29} \approx 2.724137931$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Use the distributive property to multiply -\frac{3}{2} by 3x-5.

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

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

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

Multiply -3 and 3 to get -9.

$$\frac{2}{3}-\frac{1}{3}x+\frac{-9}{2}x-\frac{3}{2}\left(-5\right)=-5$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$\frac{2}{3}-\frac{1}{3}x-\frac{9}{2}x-\frac{3}{2}\left(-5\right)=-5$$

Express -\frac{3}{2}\left(-5\right) as a single fraction.

$$\frac{2}{3}-\frac{1}{3}x-\frac{9}{2}x+\frac{-3\left(-5\right)}{2}=-5$$

Multiply -3 and -5 to get 15.

$$\frac{2}{3}-\frac{1}{3}x-\frac{9}{2}x+\frac{15}{2}=-5$$

Combine -\frac{1}{3}x and -\frac{9}{2}x to get -\frac{29}{6}x.

$$\frac{2}{3}-\frac{29}{6}x+\frac{15}{2}=-5$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{15}{2} to fractions with denominator 6.

$$\frac{4}{6}-\frac{29}{6}x+\frac{45}{6}=-5$$

Since \frac{4}{6} and \frac{45}{6} have the same denominator, add them by adding their numerators.

$$\frac{4+45}{6}-\frac{29}{6}x=-5$$

Add 4 and 45 to get 49.

$$\frac{49}{6}-\frac{29}{6}x=-5$$

Subtract \frac{49}{6} from both sides.

$$-\frac{29}{6}x=-5-\frac{49}{6}$$

Convert -5 to fraction -\frac{30}{6}.

$$-\frac{29}{6}x=-\frac{30}{6}-\frac{49}{6}$$

Since -\frac{30}{6} and \frac{49}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{29}{6}x=\frac{-30-49}{6}$$

Subtract 49 from -30 to get -79.

$$-\frac{29}{6}x=-\frac{79}{6}$$

Multiply both sides by -\frac{6}{29}, the reciprocal of -\frac{29}{6}.

$$x=-\frac{79}{6}\left(-\frac{6}{29}\right)$$

Multiply -\frac{79}{6} times -\frac{6}{29} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-79\left(-6\right)}{6\times 29}$$

Do the multiplications in the fraction \frac{-79\left(-6\right)}{6\times 29}.

$$x=\frac{474}{174}$$

Reduce the fraction \frac{474}{174} to lowest terms by extracting and canceling out 6.

$$x=\frac{79}{29}$$