Solve 1/2(3x-1)=1/5(4x+2)-1

$$\frac{ 1 }{ 2 } (3x-1)= \frac{ 1 }{ 5 } (4x+2)-1$$

Solve for x

$$x=-\frac{1}{7}\approx -0.142857143$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}\times 3x+\frac{1}{2}\left(-1\right)=\frac{1}{5}\left(4x+2\right)-1$$

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

$$\frac{3}{2}x+\frac{1}{2}\left(-1\right)=\frac{1}{5}\left(4x+2\right)-1$$

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

$$\frac{3}{2}x-\frac{1}{2}=\frac{1}{5}\left(4x+2\right)-1$$

Use the distributive property to multiply \frac{1}{5} by 4x+2.

$$\frac{3}{2}x-\frac{1}{2}=\frac{1}{5}\times 4x+\frac{1}{5}\times 2-1$$

Multiply \frac{1}{5} and 4 to get \frac{4}{5}.

$$\frac{3}{2}x-\frac{1}{2}=\frac{4}{5}x+\frac{1}{5}\times 2-1$$

Multiply \frac{1}{5} and 2 to get \frac{2}{5}.

$$\frac{3}{2}x-\frac{1}{2}=\frac{4}{5}x+\frac{2}{5}-1$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{3}{2}x-\frac{1}{2}=\frac{4}{5}x+\frac{2}{5}-\frac{5}{5}$$

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

$$\frac{3}{2}x-\frac{1}{2}=\frac{4}{5}x+\frac{2-5}{5}$$

Subtract 5 from 2 to get -3.

$$\frac{3}{2}x-\frac{1}{2}=\frac{4}{5}x-\frac{3}{5}$$

Subtract \frac{4}{5}x from both sides.

$$\frac{3}{2}x-\frac{1}{2}-\frac{4}{5}x=-\frac{3}{5}$$

Combine \frac{3}{2}x and -\frac{4}{5}x to get \frac{7}{10}x.

$$\frac{7}{10}x-\frac{1}{2}=-\frac{3}{5}$$

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

$$\frac{7}{10}x=-\frac{3}{5}+\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert -\frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{7}{10}x=-\frac{6}{10}+\frac{5}{10}$$

Since -\frac{6}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{7}{10}x=\frac{-6+5}{10}$$

Add -6 and 5 to get -1.

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

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

$$x=-\frac{1}{10}\times \frac{10}{7}$$

Multiply -\frac{1}{10} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 10 in both numerator and denominator.

$$x=\frac{-1}{7}$$

Fraction \frac{-1}{7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$x=-\frac{1}{7}$$