Solving Equations with Variables on Both Sides

1. (g+4) - 3g = 1 + g

g = 1

g = 4

no solution

identity

2. - 6a + 3 = - 3 (2a - 1)

a=5

a=10

no solution

identity

3. 0.5b + 4 = 2 (b+2)

b=0

b=0.5

no solution

identity

4. 8 - (3 + b) = b - 9

7

8

no solution

identity

1)

g+4-3g=1+g

subtracting g from both sides

4-3g=1

subtracting 4 from both sides

-3g=-3

g=1

2)

-6a+3=-3 (2a-1)

extending the right side

-6a+3=-6a+3

adding 6a to both sides

3=3

which is an identity

3)

0.5b+4=2 (b+2)

extending the right side

0.5b+4=2b+4

subtracting 0.5 b from both sides

4=1.5b+4

subtracting 4 from both sides

0=1.5b

b=0

4)

8 - (3+b) = b-9

subtracting 8 from both sides

- (3+b) = b-17

extending the left side

-3-b=b-17

adding b to both sides

-3=2b-17

adding 17 to both sides

14=2b

b=7