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

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

Solve for x

$$x = -\frac{8}{5} = -1\frac{3}{5} = -1.6$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by x+2.

$$7x+14-5\left(x-6\right)=12\left(x+5\right)$$

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

$$7x+14-5x+30=12\left(x+5\right)$$

Combine 7x and -5x to get 2x.

$$2x+14+30=12\left(x+5\right)$$

Add 14 and 30 to get 44.

$$2x+44=12\left(x+5\right)$$

Use the distributive property to multiply 12 by x+5.

$$2x+44=12x+60$$

Subtract 12x from both sides.

$$2x+44-12x=60$$

Combine 2x and -12x to get -10x.

$$-10x+44=60$$

Subtract 44 from both sides.

$$-10x=60-44$$

Subtract 44 from 60 to get 16.

$$-10x=16$$

Divide both sides by -10.

$$x=\frac{16}{-10}$$

Reduce the fraction \frac{16}{-10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{8}{5}$$