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

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

Solve for x

$$x=-7$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x+5.

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

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

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

Express \frac{2}{5}\left(-3\right) as a single fraction.

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

Multiply 2 and -3 to get -6.

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

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

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

Subtract \frac{2}{5}x from both sides.

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

Combine 2x and -\frac{2}{5}x to get \frac{8}{5}x.

$$\frac{8}{5}x+10=-\frac{6}{5}$$

Subtract 10 from both sides.

$$\frac{8}{5}x=-\frac{6}{5}-10$$

Convert 10 to fraction \frac{50}{5}.

$$\frac{8}{5}x=-\frac{6}{5}-\frac{50}{5}$$

Since -\frac{6}{5} and \frac{50}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{5}x=\frac{-6-50}{5}$$

Subtract 50 from -6 to get -56.

$$\frac{8}{5}x=-\frac{56}{5}$$

Multiply both sides by \frac{5}{8}, the reciprocal of \frac{8}{5}.

$$x=-\frac{56}{5}\times \frac{5}{8}$$

Multiply -\frac{56}{5} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-56\times 5}{5\times 8}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{-56}{8}$$

Divide -56 by 8 to get -7.

$$x=-7$$