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

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply -\frac{1}{5} by x+2.

$$\frac{1}{2}x-\frac{1}{2}=2-\frac{1}{5}x-\frac{1}{5}\times 2$$

Express -\frac{1}{5}\times 2 as a single fraction.

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

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

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

Convert 2 to fraction \frac{10}{5}.

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

Since \frac{10}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 10 to get 8.

$$\frac{1}{2}x-\frac{1}{2}=\frac{8}{5}-\frac{1}{5}x$$

Add \frac{1}{5}x to both sides.

$$\frac{1}{2}x-\frac{1}{2}+\frac{1}{5}x=\frac{8}{5}$$

Combine \frac{1}{2}x and \frac{1}{5}x to get \frac{7}{10}x.

$$\frac{7}{10}x-\frac{1}{2}=\frac{8}{5}$$

Add \frac{1}{2} to both sides.

$$\frac{7}{10}x=\frac{8}{5}+\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{8}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{7}{10}x=\frac{16}{10}+\frac{5}{10}$$

Since \frac{16}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{7}{10}x=\frac{16+5}{10}$$

Add 16 and 5 to get 21.

$$\frac{7}{10}x=\frac{21}{10}$$

Multiply both sides by \frac{10}{7}, the reciprocal of \frac{7}{10}.

$$x=\frac{21}{10}\times \frac{10}{7}$$

Multiply \frac{21}{10} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{21\times 10}{10\times 7}$$

Cancel out 10 in both numerator and denominator.

$$x=\frac{21}{7}$$

Divide 21 by 7 to get 3.

$$x=3$$