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Solve:
Both sides of the equation have expressions that we should simplify before we isolate the variable.
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| Distribute on the left, subtract on the right. |
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| Use the Commutative Property of Addition. |
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| Combine like terms. |
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| Undo subtraction by using the Addition Property of Equality. |
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| Simplify. |
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| Check.
Let 
The solution checks. |
In previous chapters, we translated word sentences into equations. The first step is to look for the word (or words) that translate(s) to the equal sign. [link] reminds us of some of the words that translate to the equal sign.
| Equals (=) | ||||||
|---|---|---|---|---|---|---|
| is | is equal to | is the same as | the result is | gives | was | will be |
Let’s review the steps we used to translate a sentence into an equation.
Now we are ready to try an example.
Translate and solve: five more than is equal to
| Translate. |
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| Subtract 5 from both sides. |
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| Simplify. |
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| Check:
Is five more than ? 
The solution checks. |
Translate and solve: Eleven more than is equal to
x + 11 = 41; x = 30
Translate and solve: Twelve less than is equal to
y − 12 = 51; y = 63
Translate and solve: The difference of and is
| Translate. |
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| Simplify. |
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Check:
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| The solution checks. |
Translate and solve: The difference of and is
4 x − 3 x = 14; x = 14
Translate and solve: The difference of and is
7 a − 6 a = −8; a = −8
In most of the application problems we solved earlier, we were able to find the quantity we were looking for by simplifying an algebraic expression. Now we will be using equations to solve application problems. We’ll start by restating the problem in just one sentence, assign a variable, and then translate the sentence into an equation to solve. When assigning a variable, choose a letter that reminds you of what you are looking for.
The Robles family has two dogs, Buster and Chandler. Together, they weigh pounds.
Chandler weighs pounds. How much does Buster weigh?
| Read the problem carefully. | |
| Identify what you are asked to find, and choose a variable to represent it. | How much does Buster weigh?
Let Buster's weight |
| Write a sentence that gives the information to find it. | Buster's weight plus Chandler's weight equals 71 pounds. |
| We will restate the problem, and then include the given information. | Buster's weight plus 28 equals 71. |
| Translate the sentence into an equation, using the variable . |
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| Solve the equation using good algebraic techniques. |
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| Check the answer in the problem and make sure it makes sense. | |
| Is 43 pounds a reasonable weight for a dog? Yes. Does Buster's weight plus Chandler's weight equal 71 pounds? | |
| Write a complete sentence that answers the question, "How much does Buster weigh?" | Buster weighs 43 pounds |
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