Question

Which equation has infinitely many solutions?

5(2x + 4) = 10x - 12
5(2x + 4) = 10(x + 2)
5(2x + 4) = 12x
5(2x + 10) = 20(x + 1)

Answer 1

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

Explanation:

An equation has infinitely many solutions when they end in 0 = 0, that is, both sides are exactly equivalent. In this case, basically, all real numbers are solution, it's like a line under the same line, it's like the reflexive property, every number is equal to itself.

The expression that fulfil that definition is the second one, because:

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

10x + 20 = 10x + 20

10x - 10x = 20 - 20x

0 = 0

Therefore, it's demonstrated that the second equation has infinite solutions, that is, all numbers are solutions.

Answer 2

B.

Explanation:

If you distribute 5(2x+4) which gives you 10x+20 and if you distribute 10(x+2) you get 10x+20 and they are both the same which means it has infinitely many solutions.

*Same slope same y-intercept (infinitely many solutions).

*Same slope different y-intercept (No solution).

*Different slope same y-intercept (One solution).

*Different slope different y-intercept (One solution).