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

$$x - ( 2 x - 5 ) = 1 - 3 ( 2 - x )$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

To find the opposite of 2x-5, find the opposite of each term.

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

The opposite of -5 is 5.

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

Combine x and -2x to get -x.

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

Use the distributive property to multiply -3 by 2-x.

$$-x+5=1-6+3x$$

Subtract 6 from 1 to get -5.

$$-x+5=-5+3x$$

Subtract 3x from both sides.

$$-x+5-3x=-5$$

Combine -x and -3x to get -4x.

$$-4x+5=-5$$

Subtract 5 from both sides.

$$-4x=-5-5$$

Subtract 5 from -5 to get -10.

$$-4x=-10$$

Divide both sides by -4.

$$x=\frac{-10}{-4}$$

Reduce the fraction \frac{-10}{-4} to lowest terms by extracting and canceling out -2.

$$x=\frac{5}{2}$$