Solve 2left(x-5right)-1left(x-2right)=-3/2

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

Solve for x

$$x = \frac{13}{2} = 6\frac{1}{2} = 6.5$$

Steps for Solving Linear Equation

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

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

To find the opposite of x-2, find the opposite of each term.

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

The opposite of -2 is 2.

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

Combine 2x and -x to get x.

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

Add -10 and 2 to get -8.

$$x-8=-\frac{3}{2}$$

Add 8 to both sides.

$$x=-\frac{3}{2}+8$$

Convert 8 to fraction \frac{16}{2}.

$$x=-\frac{3}{2}+\frac{16}{2}$$

Since -\frac{3}{2} and \frac{16}{2} have the same denominator, add them by adding their numerators.

$$x=\frac{-3+16}{2}$$

Add -3 and 16 to get 13.

$$x=\frac{13}{2}$$