Algebra - Adding To Both Sides of the Equation

You are always allowed to add the same number to both sides of an equation.

To find out the value of x, we want to "isolate" it (have it alone on one side of the equation).

Example 1

x − 3 = 5

In this example, x is already on the left side. We want to get rid of the (−3) on the left side. To do so, we can add 3. However, if we add 3 to the left side of the equation, we must add 3 to the right side of the equation, so that the equation remains balanced:

(x − 3) + 3 = (5) + 3

x − 3 + 3 = 5 + 3

x = 8

Try the following examples on your own:

  1. x − 12 = 17
  2. 15 = x − 7

Example 2

x + 3 = 5

In this example, x is already on the left side. We want to get rid of the (+3) on the left side. To do so, we can add −3. However, if we add -3 to the left side of the equation, we must add −3 to the right side of the equation, so that the equation remains balanced:

(x + 3) + −3 = (5) + −3

x − 3 + 3 = 5 + −3

x = 2

Note that instead of subtracting 3, we add −3. This helps to prevent stupid mistakes when doing more complicated algebra. The general rule is:

Subtracting is the same as adding the opposite.

Try the following examples on your own:

  1. x + 12 = 17
  2. 4 = x + 24
Homework

You can work with a friend, but each of you must submit your own work.

Solve for x.

  1. x − 17 = 31
  2. x + 12 = −5
  3. x + B = C
  4. x + 9 = 2x + 8
  5. 9x = 10x + 3

Question and Answer Generator

If you download this spreadsheet, you can generate as many of these types of problems as you want to practice.

Pressing F9 (or under the "Data" menu, "Refresh All Connections") will generate new problems using random integers.