Question

Decide whether each equation has one solution, no solution or infinitely many solutions

2(x - 3) = 2x

3(y - 3) = 2y - 9 + y

10x - 2 - 6x = 3x - 2 + x

4(x + 3) + 2x = x - 8

Please Show how you did it if possible please thanks! :)

Answer 1

1st:
2(x-3) = 2x
2x - 6 = 2x
-6 = 0 -----> contradiction, thus no solution


4th:
4(x+3) + 2x = x - 8
4x + 12 + 2x = x - 8
5x = -20
x = -4 -----> One solution

in general
- if you get ?x = ? , there will be one solution
- if the variable drops out, and you get a true statement, there will be an infinite number of solutions
- if the variable drops out, and you get a false statement, such as #1, there will be no solution.

Use these rules to answer the other 2 questions.