GED Mathematical Reasoning: Equations II – Adding and Subtracting

Example 1

Solve the equation and check your answer:  n + 3.2 = 5.4

 

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

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The solution, then is n = 2.2. 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.

n + 3.2 = 5.4
(2.2) + 3.2 = 5.4
5.4 = 5.4

 

Example 2

Solve the equation and check your answer: y + \frac{1}{4} = 3

 

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 \frac{1}{4} is addition. Therefore to solve for “y,” we will do the opposite operation and subtract \frac{1}{4} from both sides.

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On the left side, \frac{1}{4} minus \frac{1}{4} equals zero, leaving just “y.”

On the right side, we need to subtract \frac{1}{4} from 3. It is good to review subtracting with fractions, so let’s do this by hand.

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We’ll need a common denominator, which will be 4. \frac{1}{4} already has a denominator of 4, so let’s focus on the number 3. We’ll first write it as: \frac{3}{1}. Then, we’ll multiply both the numerator and denominator by 4. So the value of 3, with a denominator of 4 becomes: \frac{12}{4}

3 = \frac{3}{1} \rightarrow \frac{3 \cdot 4}{1 \cdot 4} = \frac{12}{4}

Now we’re ready to subtract \frac{1}{4} from \frac{12}{4} 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:  y = \frac{11}{4}.

\frac{12}{4} - \frac{1}{4} = \frac{12 - 1}{4} = \frac{11}{4}

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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 \frac{11}{4} plus \frac{1}{4} equal to 3? Well, \frac{11}{4} plus \frac{1}{4} equals \frac{12}{4} , which reduces to 3 (since 12 divided by 4 is 3). So our solution checks out!

y + \frac{1}{4} = 3

\frac{11}{4} + \frac{1}{4} = 3

\frac{11 + 1}{4} = 3

\frac{12}{4} = 3

3 = 3

 

Example 3

Solve the equation and check your answer: n - \$12 = \$38

 

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.

The addition and subtraction undo each other on the left side, leaving just “n.”

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.

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As a final check, we’ll substitute n = \$50 back into the original equation to verify that the statement is true. Since $50 minus $12 equals $38, our solution checks out!

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