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Which equation below has infinite solutions?

A) 2x + 5 = 2x + 8
B) 5x – 1= 2x + 4
C) x + 9 = x + 9
D) 4x 1 = 6x + 2

User Cmyr
by
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1 Answer

4 votes

Answer:

C) x + 9 = x + 9

Explanation:

An equation has infinite solutions if can simplify to the format: a = a, where a is any number.

This is because it means that any value you plug into x will give you the same true equation and answer.

C meets these requirements as it is already in format a=a, but if we further simplify it, we can see how it works:

Subtract x from both sides: 9=9

Subtract 9 from both sides: x=x

Subtract (x+9) from both sides: 0=0

We can see that C has infinite solutions because any value you put in for x, it will cancel itself out when you solve it, therefore it has infinite solutions.

E.g. x=5

(5) + 9 = (5) + 9

14 = 14

E.g. x=-25

(-25) + 9 = (-25) = 9

-16 = -16

We can also answer this question by solving all the other equations:

A) 2x + 5 - 2x = 2x - 2x + 8

5 = 8

This is not true so this equation has NO solutions.

B) 5x - 2x - 1 = 2x - 2x + 4

3x - 1 + 1 = 4 + 1

3x = 5

x = 5/3 (One solution)

D) I think you've missed a sign here, but it is solvable either way to get to one solution.

Hope this helped!

User Salamey
by
5.4k points