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

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{5} by 3x+4.

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

Multiply \frac{1}{5} and 3 to get \frac{3}{5}.

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

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

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

Combine 3x and \frac{3}{5}x to get \frac{18}{5}x.

$$\frac{18}{5}x-5+\frac{4}{5}=2x-1$$

Convert -5 to fraction -\frac{25}{5}.

$$\frac{18}{5}x-\frac{25}{5}+\frac{4}{5}=2x-1$$

Since -\frac{25}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$\frac{18}{5}x+\frac{-25+4}{5}=2x-1$$

Add -25 and 4 to get -21.

$$\frac{18}{5}x-\frac{21}{5}=2x-1$$

Subtract 2x from both sides.

$$\frac{18}{5}x-\frac{21}{5}-2x=-1$$

Combine \frac{18}{5}x and -2x to get \frac{8}{5}x.

$$\frac{8}{5}x-\frac{21}{5}=-1$$

Add \frac{21}{5} to both sides.

$$\frac{8}{5}x=-1+\frac{21}{5}$$

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

$$\frac{8}{5}x=-\frac{5}{5}+\frac{21}{5}$$

Since -\frac{5}{5} and \frac{21}{5} have the same denominator, add them by adding their numerators.

$$\frac{8}{5}x=\frac{-5+21}{5}$$

Add -5 and 21 to get 16.

$$\frac{8}{5}x=\frac{16}{5}$$

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

$$x=\frac{16}{5}\times \frac{5}{8}$$

Multiply \frac{16}{5} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{16\times 5}{5\times 8}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{16}{8}$$

Divide 16 by 8 to get 2.

$$x=2$$