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

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

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

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

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

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

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

Convert 3 to fraction \frac{6}{2}.

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

Since -\frac{5}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

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

Add -5 and 6 to get 1.

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

Subtract 2x from both sides.

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

Combine \frac{5}{2}x and -2x to get \frac{1}{2}x.

$$\frac{1}{2}x+\frac{1}{2}=-1$$

Subtract \frac{1}{2} from both sides.

$$\frac{1}{2}x=-1-\frac{1}{2}$$

Convert -1 to fraction -\frac{2}{2}.

$$\frac{1}{2}x=-\frac{2}{2}-\frac{1}{2}$$

Since -\frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x=\frac{-2-1}{2}$$

Subtract 1 from -2 to get -3.

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

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

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

Cancel out 2 and 2.

$$x=-3$$