Solve 4(x-2)-5(x-6)=2(x+1)+3(2x+3)

$$4 ( x - 2 ) - 5 ( x - 6 ) = 2 ( x + 1 ) + 3 ( 2 x + 3 )$$

Solve for x

$$x = \frac{11}{9} = 1\frac{2}{9} \approx 1.222222222$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by x-2.

$$4x-8-5\left(x-6\right)=2\left(x+1\right)+3\left(2x+3\right)$$

Use the distributive property to multiply -5 by x-6.

$$4x-8-5x+30=2\left(x+1\right)+3\left(2x+3\right)$$

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

$$-x-8+30=2\left(x+1\right)+3\left(2x+3\right)$$

Add -8 and 30 to get 22.

$$-x+22=2\left(x+1\right)+3\left(2x+3\right)$$

Use the distributive property to multiply 2 by x+1.

$$-x+22=2x+2+3\left(2x+3\right)$$

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

$$-x+22=2x+2+6x+9$$

Combine 2x and 6x to get 8x.

$$-x+22=8x+2+9$$

Add 2 and 9 to get 11.

$$-x+22=8x+11$$

Subtract 8x from both sides.

$$-x+22-8x=11$$

Combine -x and -8x to get -9x.

$$-9x+22=11$$

Subtract 22 from both sides.

$$-9x=11-22$$

Subtract 22 from 11 to get -11.

$$-9x=-11$$

Divide both sides by -9.

$$x=\frac{-11}{-9}$$

Fraction \frac{-11}{-9} can be simplified to \frac{11}{9} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{11}{9}$$