Question

Which describes the first step in solving the equation x-5=15? A. Add 5 to each side B. Add 12 to each side C. Subtract 5 from each side D. Subtract 12 from each side

Answer 1

A.

Explanation:

If you have an equation it simply means that the left side of the equals sign is equal to the right side.

If you do the same thing to both sides of an equation then they both change by the same amount so remain equal.

[example: 5 apples = 5 apples (obviously true).

Add 2 pears to left side 5 apples + 2 pears `!=` 5 apples (no longer equal!)

If we also add 2 pears to the other side then the sides remain equal

5 apples + 2 pears `=` 5 apples + 2 pears # ]

A letter (e.g. `x`) can be used to represent a number that we don't know the value of yet.

It's not really as mysterious as it looks. If we have enough information we can "solve" for the unknown (find it's value).

To solve for an unknown it is helpful to rearrange (by doing the same to both sides at each step) so that only the unknown is on one side (so we get an equation for what it equals).

In this case (`x-5=15`) the first thing to do is to cancel out the `-5` on the left side.

To do this we can add 5 to the left side

`x - 5 + 5 = x`

For the equation to remain equal both sides we must also add 5 to the other side.

So the answer is A.