5 ( x + 2 ) = 5(x+2)= 5 x + 10 5x+10 Determined whether it has one solution, infinite number of solution , or no solutions

Answer 1

So, if we end up with x = something, we have one answer. If we end up with an untrue equation, like 0 = 5, we have no solution, but if we end up with 0 = 0, we have infinite solutions.

5(x + 2) = 5x + 10

Because 5 is a factor being multiplied by x + 2, we can divide both sides by 5.

x + 2 = x + 2

x = x

0 = 0

Well, there ya go. We have an infinite number of solutions. No matter what value we give x, the equation will be true.

Let's try other examples.

5(x + 3) = 5x + 10

x + 3 = x + 2

x = x - 1

0 = -1

Well, that's not true, so we have no solution. We can't find any value for x to make the equation true.

5(x + 2) = 20

x + 2 = 4

x = 2

Hey, this has one solution that makes the equation true. Any other value for x would not make our equation true.

Hope this helps!

Answer 2

This question is a little confusing, but I believe the solution is infinite as you can prove it is true for all numbers (if I understood your question correctly). See below:

5(x+2) = 5x+10

(Distribute)

5x + 10 = 5x +10

∴It is true for all cases.

You can take this one step further and subtract 5x + 10 from both sides to get 0 = 0, a statement that always holds true.