More than one answer for writing a pronumeral equation

[Skye8886]

Hi! I am Skye, I am 9 and my Mum is getting me to do maths from higher grades as extension.

I have a question about writing an equation to find the value of a pronumeral.

Can an algebraic equation with an unknown pronumeral have two answers (and therefor two equations)?

For this question, 'I think of a number, double it, and add 5 and I get an answer of 11' I have come up with -

2 (x + 5) = 11
=2x + 10 = 11
= 1
= 2x (over) 2 = 1 (over) 2
= 0.5

And -
2x + 5 = 11
2x = 11 - 5
2x = 6
x = 6 / 2
x = 3

If you check both add back up to 11. Someone said that my first answer isn't correct as an equation. I am confused by this because they both get the answer of 11 which is what is says in the word problem.

Please help.

Thanks,

Skye

 

[Dr.Peterson]

Hi, Skye.

These are two different equations, but only the second accurately represents your sentence (word problem).

In the first, the expression on the left says to first add 5, and then double the result, which is not what the sentence says.

So if our number is 0.5, we can double it to get 1, then add 5 to get 6, not 11.

The second equation is correct; if we pick 3, we double it to get 6, then add 5 to get 11. That solution works.

 

[JeffM]

Hi Skye

In answer to your first question, an equation may have more than one valid solution. The kind of equation that you are considering, however, is called a linear equation. Such equations may have no valid solution, exactly one valid solution, or an infinite number of valid solutions. A different type of equation called quadratic may have no real solution, one real solution, or two real solutions. In short, the number of valid solutions depends on the type of equation.

Both of your equations are valid equations, and you have found correct solutions to both.

However, as Dr. Peterson pointed out, only one of your equations is a correct translation of your word problem.