X+x+2+x=144

Question

introduction to problem solving

 

Answer 1

x + x + 2 + x = 144

3x + 2 = 144

3x = 142

x = 47 1/3

Answer 2

This looks much more confusing than it really is. Let's look at the problem step-by-step and I'll explain it as I go along.

First, you have x that stand for a number that is unknown for now, but look closly at the problem. You have more than 1 x, and they are all being added. So we can use the associative property of addition to combine all of these like terms.

It will look like this

(x + x) + 2 + (x) = 144

you have 3 x's so we write 3x

3x + 2 = 144

Now we can solve for x. We know that when we add 2 and the number that results from multiplying 3 and x we will get 144. So we need to balance this equation to have all the constant numbers (the ones we know) on one side of the equal sign and the variable (the x) on the other. We start with the +2. In order bring that +2 back to 0 we must subtract 2, so we do that for both sides of the equation. It looks like this:

3x + 2 = 144

     -2        -2

      3x = 142

So now we are left knowing that a number times 3 equals 142. Since we know that division is the opposite of multiplication we can say that 142 divided by 3 equals x. This is how it looks:

   3x = 142

   3        3

x = 142/3

142/3 = 47.333333... this is an irrational number because it never resolves. Another way we can "solve" or simplify our answer is to look at it like a fraction. 142/3 = 47 R 1. The remainder becomes the numerator of the denominator 3. So the answer would like this: x = 47 1/3

The second answer is much easier to work with if you want to check your work. Whenever you solve an equation, you can always check your answer by plugging your results into the equation wherever the variable is expressed. So here is the original equation again:

x + x + 2 + x = 144

We found that x = 47 1/3 so:

47 1/3 + 487 1/3+ 2 + 47 1/3 =? 144

Let's group these together to make adding easier: (47 1/3+47 1/3) + (2+47 1/3) =? 144

94 2/3 + 49 1/3 = 143 3/3 the 3/3 simplifies to 1, and when added to 143 equals 144. So our answer      x = 47 1/3 is correct because it justifies the equation.