Solve 1/3(x-5)+2/3=1/3(6x-5)+5/2

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

Solve for x

$$x = -\frac{11}{10} = -1\frac{1}{10} = -1.1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x-5.

$$\frac{1}{3}x+\frac{1}{3}\left(-5\right)+\frac{2}{3}=\frac{1}{3}\left(6x-5\right)+\frac{5}{2}$$

Multiply \frac{1}{3} and -5 to get \frac{-5}{3}.

$$\frac{1}{3}x+\frac{-5}{3}+\frac{2}{3}=\frac{1}{3}\left(6x-5\right)+\frac{5}{2}$$

Fraction \frac{-5}{3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$\frac{1}{3}x-\frac{5}{3}+\frac{2}{3}=\frac{1}{3}\left(6x-5\right)+\frac{5}{2}$$

Since -\frac{5}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}x+\frac{-5+2}{3}=\frac{1}{3}\left(6x-5\right)+\frac{5}{2}$$

Add -5 and 2 to get -3.

$$\frac{1}{3}x+\frac{-3}{3}=\frac{1}{3}\left(6x-5\right)+\frac{5}{2}$$

Divide -3 by 3 to get -1.

$$\frac{1}{3}x-1=\frac{1}{3}\left(6x-5\right)+\frac{5}{2}$$

Use the distributive property to multiply \frac{1}{3} by 6x-5.

$$\frac{1}{3}x-1=\frac{1}{3}\times 6x+\frac{1}{3}\left(-5\right)+\frac{5}{2}$$

Multiply \frac{1}{3} and 6 to get \frac{6}{3}.

$$\frac{1}{3}x-1=\frac{6}{3}x+\frac{1}{3}\left(-5\right)+\frac{5}{2}$$

Divide 6 by 3 to get 2.

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

Multiply \frac{1}{3} and -5 to get \frac{-5}{3}.

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

Fraction \frac{-5}{3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

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

Least common multiple of 3 and 2 is 6. Convert -\frac{5}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{1}{3}x-1=2x-\frac{10}{6}+\frac{15}{6}$$

Since -\frac{10}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}x-1=2x+\frac{-10+15}{6}$$

Add -10 and 15 to get 5.

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

Subtract 2x from both sides.

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

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

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

Add 1 to both sides.

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

Convert 1 to fraction \frac{6}{6}.

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

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

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

Add 5 and 6 to get 11.

$$-\frac{5}{3}x=\frac{11}{6}$$

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

$$x=\frac{11}{6}\left(-\frac{3}{5}\right)$$

Multiply \frac{11}{6} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{11\left(-3\right)}{6\times 5}$$

Do the multiplications in the fraction \frac{11\left(-3\right)}{6\times 5}.

$$x=\frac{-33}{30}$$

Reduce the fraction \frac{-33}{30} to lowest terms by extracting and canceling out 3.

$$x=-\frac{11}{10}$$