Solve -4x+5(2-x)-7=4(x-3)-3(x+1)

$$- 4 x + 5 ( 2 - x ) - 7 = 4 ( x - 3 ) - 3 ( x + 1 )$$

Solve for x

$$x = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

Steps for Solving Linear Equation

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

$$-4x+10-5x-7=4\left(x-3\right)-3\left(x+1\right)$$

Combine -4x and -5x to get -9x.

$$-9x+10-7=4\left(x-3\right)-3\left(x+1\right)$$

Subtract 7 from 10 to get 3.

$$-9x+3=4\left(x-3\right)-3\left(x+1\right)$$

Use the distributive property to multiply 4 by x-3.

$$-9x+3=4x-12-3\left(x+1\right)$$

Use the distributive property to multiply -3 by x+1.

$$-9x+3=4x-12-3x-3$$

Combine 4x and -3x to get x.

$$-9x+3=x-12-3$$

Subtract 3 from -12 to get -15.

$$-9x+3=x-15$$

Subtract x from both sides.

$$-9x+3-x=-15$$

Combine -9x and -x to get -10x.

$$-10x+3=-15$$

Subtract 3 from both sides.

$$-10x=-15-3$$

Subtract 3 from -15 to get -18.

$$-10x=-18$$

Divide both sides by -10.

$$x=\frac{-18}{-10}$$

Reduce the fraction \frac{-18}{-10} to lowest terms by extracting and canceling out -2.

$$x=\frac{9}{5}$$