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

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

Solve for x

$$x = -\frac{12}{5} = -2\frac{2}{5} = -2.4$$

Steps for Solving Linear Equation

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

$$7-\left(-x\right)-\left(-5\right)=2\left(x+3\right)-6\left(x+1\right)$$

The opposite of -5 is 5.

$$7-\left(-x\right)+5=2\left(x+3\right)-6\left(x+1\right)$$

Add 7 and 5 to get 12.

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

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

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

Use the distributive property to multiply -6 by x+1.

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

Combine 2x and -6x to get -4x.

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

Subtract 6 from 6 to get 0.

$$12-\left(-x\right)=-4x$$

Add 4x to both sides.

$$12-\left(-x\right)+4x=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

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

Multiply -1 and -1 to get 1.

$$x+4x=-12$$

Combine x and 4x to get 5x.

$$5x=-12$$

Divide both sides by 5.

$$x=\frac{-12}{5}$$

Fraction \frac{-12}{5} can be rewritten as -\frac{12}{5} by extracting the negative sign.

$$x=-\frac{12}{5}$$