Question

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

Answer 1

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