Answer:
A) One solution
B) No solution
C) Infinite number of solutions
D) One solution
E) Infinite number of solutions
Explanation:
There are 5 equations to solve:
A) - 4 x + 6 + 3 x = -12
combining like terms and solving for x gives:
- x + 6 = - 12
- x = -18
x = 18
which is a unique (ONE) solution
B) 5 (2 x - 2) = 10 x + 10
distributive property gives us: 10 x - 10 = 10 x + 10
then subtract 10 x from both sides and we get: -10 = 10 which is an absurd, therefore this equation has NO SOLUTION.
C) 6 x + 2 x - 8 = 8 (x - 1)
Combining like terms and using distributive property, we get:
8 x - 8 = 8 x - 8
which is an identity, So this is true for all possible x values, then the are INFINITE NUMBER OF SOLUTIONS
D) 2 x + 50 = 90
solving for x gives:
2 x = 40
x = 40/2
x = 20
which is a unique (ONE) solution.
E) 2 (x - 4) = 2 x + 10 - 18
Using distributive property and combining like terms we get:
2 x - 8 = 2 x -8
This is an identity which will give true for all real x-values. Therefore it has INFINITE NUMBER OF SOLUTIONS.