Question

A number is increased by 2 and then multiplied by 3. The result is 24. What is this number?

Answer 1

Answer:

Because you don't know what number this is, let it be represented by a variable, like x.

First, write out what is being done to the number.

For one, it is being increased by 2, so we can write:

x + 2

Now, we know this number is being multiplied by 3, so we can write:  

3(x + 2).  Notice the (x + 2) is in parentheses. This is important, because it tells us FIRST need to increase x by 2, and THEN multiply that number by 3. Another way to think about this is to treat (x + 2) as the number you want to multiply by 3.

Now, we know that after all this is done, it should equal 24, so we write:

3(x + 2) = 24

Now that we have our equation, let's solve for x. To do this, we want to get x by itself. So first, we'll multiply (x + 2) by 3, or in other words distribute the 3:

3(x + 2) = 24

3*x + 3*2 = 24

3x + 6 = 24

Now we have:

3x + 6 = 24

The end goal is still getting x by itself. Now we can move the 6 to the other side of the equal sign by subtracting both sides by 6.

3x + 6 - 6 = 24 - 6

3x = 18

Now because we 3x, which is 3*x, and we only want x, we can divide both sides by 3.

3x/3 = 18/3

x = 6

Step-by-step explanation: