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

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

Solve for x

$$x=-\frac{8}{59}\approx -0.13559322$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 5x-1.

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

Express \frac{2}{3}\times 5 as a single fraction.

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

Multiply 2 and 5 to get 10.

$$\frac{10}{3}x+\frac{2}{3}\left(-1\right)=-\frac{3}{5}\left(x+2\right)$$

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

$$\frac{10}{3}x-\frac{2}{3}=-\frac{3}{5}\left(x+2\right)$$

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

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

Express -\frac{3}{5}\times 2 as a single fraction.

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

Multiply -3 and 2 to get -6.

$$\frac{10}{3}x-\frac{2}{3}=-\frac{3}{5}x+\frac{-6}{5}$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$\frac{10}{3}x-\frac{2}{3}=-\frac{3}{5}x-\frac{6}{5}$$

Add \frac{3}{5}x to both sides.

$$\frac{10}{3}x-\frac{2}{3}+\frac{3}{5}x=-\frac{6}{5}$$

Combine \frac{10}{3}x and \frac{3}{5}x to get \frac{59}{15}x.

$$\frac{59}{15}x-\frac{2}{3}=-\frac{6}{5}$$

Add \frac{2}{3} to both sides.

$$\frac{59}{15}x=-\frac{6}{5}+\frac{2}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{6}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{59}{15}x=-\frac{18}{15}+\frac{10}{15}$$

Since -\frac{18}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{59}{15}x=\frac{-18+10}{15}$$

Add -18 and 10 to get -8.

$$\frac{59}{15}x=-\frac{8}{15}$$

Multiply both sides by \frac{15}{59}, the reciprocal of \frac{59}{15}.

$$x=-\frac{8}{15}\times \frac{15}{59}$$

Multiply -\frac{8}{15} times \frac{15}{59} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-8\times 15}{15\times 59}$$

Cancel out 15 in both numerator and denominator.

$$x=\frac{-8}{59}$$

Fraction \frac{-8}{59} can be rewritten as -\frac{8}{59} by extracting the negative sign.

$$x=-\frac{8}{59}$$