Solve (x+3)-7(x+5)=4(x+1)-2(x+6)+12

$$( x + 3 ) - 7 ( x + 5 ) = 4 ( x + 1 ) - 2 ( x + 6 ) + 12$$

Solve for x

$$x = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply -7 by x+5.

$$x+3-7x-35=4\left(x+1\right)-2\left(x+6\right)+12$$

Combine x and -7x to get -6x.

$$-6x+3-35=4\left(x+1\right)-2\left(x+6\right)+12$$

Subtract 35 from 3 to get -32.

$$-6x-32=4\left(x+1\right)-2\left(x+6\right)+12$$

Use the distributive property to multiply 4 by x+1.

$$-6x-32=4x+4-2\left(x+6\right)+12$$

Use the distributive property to multiply -2 by x+6.

$$-6x-32=4x+4-2x-12+12$$

Combine 4x and -2x to get 2x.

$$-6x-32=2x+4-12+12$$

Subtract 12 from 4 to get -8.

$$-6x-32=2x-8+12$$

Add -8 and 12 to get 4.

$$-6x-32=2x+4$$

Subtract 2x from both sides.

$$-6x-32-2x=4$$

Combine -6x and -2x to get -8x.

$$-8x-32=4$$

Add 32 to both sides.

$$-8x=4+32$$

Add 4 and 32 to get 36.

$$-8x=36$$

Divide both sides by -8.

$$x=\frac{36}{-8}$$

Reduce the fraction \frac{36}{-8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{9}{2}$$