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! :)
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.