Question

I am A father who needs the answer to make sure my kids did it right.Thank you Use mental math to solve each equation.Equations Question #1) x + 6 = 12Question #2) 10 - x = 2Question #3) x - 7 = 20Question #4) 4x = 20Question #5) 5 = 15 divided by xQuestion #6) 16 + x = 20Question #7) x - 4 = 6Question #8) 2x = 22Question #9) x divided by 3 = 8Question #10) 5x = 10

Answer 1

In order to solve an equation, we can apply a sequence of the same operations on both sides of the equation, until we isolate the variable x, and find its value.

We start by what numbers are on the same side as x, and apply the opposite operation in order to cancel that number on that side. For example, for Question #1, we have:

x + 6 = 12

Notice that we have a "+6" on the same side of the equation where the "x" is. So, we apply, on both sides, the operation "-6":

x + 6 - 6 = 12 - 6

x = 12 - 6

x = 6

Notice that, in practical terms, that is the same as taking out the "+6" from the left-hand side, and inserting the "-6" on the right-hand side.

So, let's use this practical rule in Question #2:

10 - x = 2

-x = 2 - 10

-x = -8

Now we multiply both sides of the equation by -1, remembering that the product of two negative numbers is a positive number:

(-1) * (-x) = (-8) * (-1)

x = 8