Solve G=-{-[-(a+b)]}-{-(-b-a)}-(a+b)

$$G = - \{ - [ - ( a + b ) ] \} - \{ - ( - b - a ) \} - ( a + b )$$

Solve for G

$$G=-3a-3b$$

Solution Steps

To find the opposite of a+b, find the opposite of each term.

$$G=-\left(-\left(-a-b\right)\right)-\left(-\left(-b-a\right)\right)-\left(a+b\right)$$

To find the opposite of -a-b, find the opposite of each term.

$$G=-\left(a+b\right)-\left(-\left(-b-a\right)\right)-\left(a+b\right)$$

To find the opposite of a+b, find the opposite of each term.

$$G=-a-b-\left(-\left(-b-a\right)\right)-\left(a+b\right)$$

To find the opposite of -b-a, find the opposite of each term.

$$G=-a-b-\left(-\left(-b\right)+a\right)-\left(a+b\right)$$

To find the opposite of -\left(-b\right)+a, find the opposite of each term.

$$G=-a-b-\left(-\left(-b\right)\right)-a-\left(a+b\right)$$

Combine -a and -a to get -2a.

$$G=-2a-b-\left(-\left(-b\right)\right)-\left(a+b\right)$$

To find the opposite of a+b, find the opposite of each term.

$$G=-2a-b-\left(-\left(-b\right)\right)-a-b$$

Combine -2a and -a to get -3a.

$$G=-3a-b-\left(-\left(-b\right)\right)-b$$

Combine -b and -b to get -2b.

$$G=-3a-2b-\left(-\left(-b\right)\right)$$

Multiply -1 and -1 to get 1.

$$G=-3a-2b-b$$

Combine -2b and -b to get -3b.

$$G=-3a-3b$$

Solve for a

$$a=-\frac{G}{3}-b$$

Steps for Solving Linear Equation

To find the opposite of a+b, find the opposite of each term.

$$G=-\left(-\left(-a-b\right)\right)-\left(-\left(-b-a\right)\right)-\left(a+b\right)$$

To find the opposite of -a-b, find the opposite of each term.

$$G=-\left(a+b\right)-\left(-\left(-b-a\right)\right)-\left(a+b\right)$$

To find the opposite of a+b, find the opposite of each term.

$$G=-a-b-\left(-\left(-b-a\right)\right)-\left(a+b\right)$$

To find the opposite of -b-a, find the opposite of each term.

$$G=-a-b-\left(-\left(-b\right)+a\right)-\left(a+b\right)$$

To find the opposite of -\left(-b\right)+a, find the opposite of each term.

$$G=-a-b-\left(-\left(-b\right)\right)-a-\left(a+b\right)$$

Combine -a and -a to get -2a.

$$G=-2a-b-\left(-\left(-b\right)\right)-\left(a+b\right)$$

To find the opposite of a+b, find the opposite of each term.

$$G=-2a-b-\left(-\left(-b\right)\right)-a-b$$

Combine -2a and -a to get -3a.

$$G=-3a-b-\left(-\left(-b\right)\right)-b$$

Combine -b and -b to get -2b.

$$G=-3a-2b-\left(-\left(-b\right)\right)$$

Swap sides so that all variable terms are on the left hand side.

$$-3a-2b-\left(-\left(-b\right)\right)=G$$

Add 2b to both sides.

$$-3a-\left(-\left(-b\right)\right)=G+2b$$

Add -\left(-b\right) to both sides.

$$-3a=G+2b-\left(-b\right)$$

Multiply -1 and -1 to get 1.

$$-3a=G+2b+b$$

Combine 2b and b to get 3b.

$$-3a=G+3b$$

Divide both sides by -3.

$$\frac{-3a}{-3}=\frac{G+3b}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$a=\frac{G+3b}{-3}$$

Divide G+3b by -3.

$$a=-\frac{G}{3}-b$$