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The techniques we have used up to now extend to more complicated expressions. Remember to follow the order of operations.
Simplify:
Simplify inside the parentheses. | |
Multiply. | |
Add left to right. |
Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers when evaluating expressions .
Evaluate
ⓐ Evaluate when | |
Simplify. |
ⓑ Evaluate when | |
Simplify. |
Evaluate each expression for the given values:
Evaluate each expression for the given values: when
When evaluate
ⓐ Evaluate when | |
Simplify. |
ⓑ Evaluate when | |
Simplify. | |
Add. |
Next we'll evaluate an expression with two variables.
Evaluate when and
This expression has two variables. Substitute
for
and
for
Add inside the parentheses. | |
Simplify |
All our earlier work translating word phrases to algebra also applies to expressions that include both positive and negative numbers. Remember that the phrase the sum indicates addition.
Translate and simplify: the sum of and
The sum of −9 and 5 indicates addition. | the sum of and |
Translate. | |
Simplify. |
Translate and simplify the expression:
the sum of and
−7 + 4 = −3
Translate and simplify the expression:
the sum of and
−8 + (−6) = −14
Translate and simplify: the sum of and increased by
The phrase increased by indicates addition.
The sum of and , increased by | |
Translate. | |
Simplify. | |
Add. |
Translate and simplify:
the sum of and increased by
[9 + (−16)] + 4 = −3
Translate and simplify:
the sum of and increased by
[−8 + (−12)] + 7 = −13
Recall that we were introduced to some situations in everyday life that use positive and negative numbers, such as temperatures, banking, and sports. For example, a debt of could be represented as Let’s practice translating and solving a few applications.
Solving applications is easy if we have a plan. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question.
The temperature in Buffalo, NY, one morning started at below zero Fahrenheit. By noon, it had warmed up What was the temperature at noon?
We are asked to find the temperature at noon.
Write a phrase for the temperature. | The temperature warmed up 12 degrees from 7 degrees below zero. |
Translate to math notation. | −7+12 |
Simplify. | 5 |
Write a sentence to answer the question. | The temperature at noon was 5 degrees Fahrenheit. |
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