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

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

Solve for x

$$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

Steps for Solving Linear Equation

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

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

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

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

Multiply 3 and 2 to get 6.

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

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

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

Multiply 3 and -5 to get -15.

$$\frac{6}{5}x+\frac{-15}{5}=1-\frac{2}{5}\left(x+1\right)$$

Divide -15 by 5 to get -3.

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

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

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

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

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

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

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

Subtract 2 from 5 to get 3.

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

Add \frac{2}{5}x to both sides.

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

Combine \frac{6}{5}x and \frac{2}{5}x to get \frac{8}{5}x.

$$\frac{8}{5}x-3=\frac{3}{5}$$

Add 3 to both sides.

$$\frac{8}{5}x=\frac{3}{5}+3$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{8}{5}x=\frac{3}{5}+\frac{15}{5}$$

Since \frac{3}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.

$$\frac{8}{5}x=\frac{3+15}{5}$$

Add 3 and 15 to get 18.

$$\frac{8}{5}x=\frac{18}{5}$$

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

$$x=\frac{18}{5}\times \frac{5}{8}$$

Multiply \frac{18}{5} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{18\times 5}{5\times 8}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{18}{8}$$

Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.

$$x=\frac{9}{4}$$