Question

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

4x + 10 = 2(2x + 5)
4x - 5 = 4x + 10
4x - 5 = -5

Answer 1

1. 4x + 10 = 2(2x + 5)
Simplify both sides:
4x + 10 = 4x + 10
Subtract 4x from both sides:
10 = 10
The equation is an identity and is true for all values of x. It has infinitely many solutions.

2. 4x - 5 = 4x + 10
Subtract 4x from both sides:
-5 = 10
The equation is a contradiction and is false for all values of x. It has no solution.

3. 4x - 5 = -5
Add 5 to both sides:
4x = 0
Divide both sides by 4:
x = 0
The equation is a conditional equation and is true for only one value of x. It has one solution.