Solving Multi-Step Equations

Question

The sum of twice a number and half the number is 10.



Equation:__=10

The number in=__

Answer 1

First we need to set up an equation to solve for the mystery number. The word "sum" indicates we will be adding the next two terms. First we have twice a number, so 2 times x or 2x. We will be adding half of the number to this, so x * 1/2 or x/2. Then we are told that the sum of these two numbers is 10, so our equation becomes

2x + x/2 = 10.

At this point we need to solve the equation. To do so, we need to first combine like terms on the left side of the equation. To add 2x and x/2 we need to have common denominators because we are adding fractions. So we multiply 2x by 2/2 to get 4x/2.

2x/2 * 2/2 + x/2 = 10

4x/2 + x/2 = 10

Now we add 4x/2 + x/2 to get 5x/2.

5x/2 = 10

Now to get x by itself we will need to multiply by the reciprocal of its coefficient, 5/2. So we multiply both sides by 2/5 to get x = 20/5.

2/5 * (5x/2) = 10 * 2/5

x = 20/5

x = 4

20/5 then simplifies to 4 which is our answer!

Answer 2

So for this one as Ashley said we get the sum of twice the number and half the number is 2x + x/2 = 10.

To remove the two from the bottom you can also just multiply both sides of the equation by 2:

2(2x + x/2) = 2*10:

4x + x = 20:

5x = 20:

x = 20/5:

x = 4