Question

Which equation has infinitely many solutions?

a. 12 + 4x = 6x + 10 – 2x
b. 5x + 14 – 4x = 23 + x – 9
c. x + 9 – 0.8x = 5.2x + 17 – 8
d. 4x – 2x = 20?

Answer 1

If you’re doing these kind of problems, you should know how to “solve for x”, so i’m just going to tell you how to do them.

All you have to do is solve for x, and if you get a number that equals itself then it is infinitely many solutions (20x=20x which is 20=20). find the answer that equals itself on both sides.

Answer 2

b. 5x + 14 – 4x = 23 + x – 9

Explanation:

a. In solving the equation we get,

12 + 4x = 6x + 10 – 2x

⇒ 4x + 12 - 10 - 4x = 0

⇒ 2 = 0

which is not true.

Thus, it has No solution.

b. 5x + 14 – 4x = 23 + x – 9

⇒ x + 14 - 14 - x = 0

⇒ 0 = 0

which is true thus it has infinite number of solution.

c. x + 9 – 0.8x = 5.2x + 17 – 8

⇒ -5.4x = 0

⇒ x = 0

Since this equation has solution thus has Single Solution.

d. 4x – 2x = 20

⇒ 2x = 20

⇒ x = 10

Since this equation has solution thus has Single Solution.