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Algebraic Equations and Inequalities

# GED Mathematical Reasoning: Equations II – Adding and Subtracting

Example 1

So to solve the equation in Example One, we’ll focus on the left side since it’s the side containing the variable. Notice that the operation between the variable and the number 3.2 is addition. So to solve for “n,” we will do the opposite operation and subtract 3.2 from both sides.

The addition and subtraction undo each other on the left side, since 3.2 minus 3.2 equals zero. This leaves just “n” on the left side.

On the right side, we need to subtract 3.2 from 5.4. The result is 2.2

The solution, then is . To check our solution, let’s substitute it back into the original equation for “n” and verify that the statement is true. Is 2.2 plus 3.2 equal to 5.4? The answer is YES! So our solution checks out.

Example 2

The variable “y” is showing on the left side, which you may be noticing is common, and the operation between the variable and the number  is addition. Therefore to solve for “y,” we will do the opposite operation and subtract  from both sides.

On the left side, minus  equals zero, leaving just “y.”

On the right side, we need to subtract  from 3. It is good to review subtracting with fractions, so let’s do this by hand.

We’ll need a common denominator, which will be 4.  already has a denominator of 4, so let’s focus on the number 3. We’ll first write it as: . Then, we’ll multiply both the numerator and denominator by 4. So the value of 3, with a denominator of 4 becomes:

Now we’re ready to subtract  from  by subtracting the numerators and keeping the common denominator. 12 minus 1 is 11. So our final solution, which is written in lowest terms, is:  .

For a check of the solution, let’s substitute it back into the original equation for “y” and verify that the statement is true. Is plus  equal to 3? Well,  plus  equals  , which reduces to 3 (since 12 divided by 4 is 3). So our solution checks out!

Example 3

Once again, the variable “n” is showing on the left side. The operation between the variable and the number $12 is subtraction. So to solve for “n,” we will add$12 to both sides.
On the right side, we will add $12 to$38, which you may do by hand or using a calculator. Either way, the result is $50. As a final check, we’ll substitute back into the original equation to verify that the statement is true. Since$50 minus $12 equals$38, our solution checks out!