Solve 1/2(3x-3)-1/5(5x-6)=0.2

$$\frac { 1 } { 2 } ( 3 x - 3 ) - \frac { 1 } { 5 } ( 5 x - 6 ) = 0.2$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}\times 3x+\frac{1}{2}\left(-3\right)-\frac{1}{5}\left(5x-6\right)=0.2$$

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

$$\frac{3}{2}x+\frac{1}{2}\left(-3\right)-\frac{1}{5}\left(5x-6\right)=0.2$$

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

$$\frac{3}{2}x+\frac{-3}{2}-\frac{1}{5}\left(5x-6\right)=0.2$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{3}{2}x-\frac{3}{2}-\frac{1}{5}\left(5x-6\right)=0.2$$

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

$$\frac{3}{2}x-\frac{3}{2}-\frac{1}{5}\times 5x-\frac{1}{5}\left(-6\right)=0.2$$

Cancel out 5 and 5.

$$\frac{3}{2}x-\frac{3}{2}-x-\frac{1}{5}\left(-6\right)=0.2$$

Express -\frac{1}{5}\left(-6\right) as a single fraction.

$$\frac{3}{2}x-\frac{3}{2}-x+\frac{-\left(-6\right)}{5}=0.2$$

Multiply -1 and -6 to get 6.

$$\frac{3}{2}x-\frac{3}{2}-x+\frac{6}{5}=0.2$$

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

$$\frac{1}{2}x-\frac{3}{2}+\frac{6}{5}=0.2$$

Least common multiple of 2 and 5 is 10. Convert -\frac{3}{2} and \frac{6}{5} to fractions with denominator 10.

$$\frac{1}{2}x-\frac{15}{10}+\frac{12}{10}=0.2$$

Since -\frac{15}{10} and \frac{12}{10} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}x+\frac{-15+12}{10}=0.2$$

Add -15 and 12 to get -3.

$$\frac{1}{2}x-\frac{3}{10}=0.2$$

Add \frac{3}{10} to both sides.

$$\frac{1}{2}x=0.2+\frac{3}{10}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x=\frac{1}{5}+\frac{3}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{3}{10} to fractions with denominator 10.

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

Since \frac{2}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

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

Add 2 and 3 to get 5.

$$\frac{1}{2}x=\frac{5}{10}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}x=\frac{1}{2}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=\frac{1}{2}\times 2$$

Cancel out 2 and 2.

$$x=1$$