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Inequalities - Values and order of operations
Order of Operations and Inequalities
There may be times when we want to compare two mathematical expressions.
For example,
True or False: 42-5(5)+4(52) is larger than or possibly equal to (9-4)(5+3(5)) ?
Solution:
Form an inequality, simplify, and determine if the answer is true or false.
Help: Order of Operations.
42-5(5)+4(52) >? (9-4)(5+3(5))
42-5(5)+4(25) >? (5)(5+15)
16-5(5)+4(25) >? (5)(20)
16-25+ 100 >? 100
16-25+ 100 >? 100
-9 + 100 >? 100
91 >? 100
Since 91 is neither greater than nor equal to 100, the statement is FALSE.
Order of Operations, Absolute Values and Inequalities
Comparing Values using Absolute Values and Inequalities
True or False: | 32 - 6(3) | is less than 23 + | -5 - 7 | ?
Solution:
Form an inequality, simplify, and determine if the result is true or false.
Help: Order of Operations, Absolute Values
| 32 - 6(3) | < ? 23 + | -5 - 7 |
| 9 - 6(3) | < ? 23 + | -5 - 7 |
| 9 - 18 | < ? 23 + | -12 |
| -9 | < ? 23 + | -12 |
9 < ? 23 + 12
9 < ? 35
The last statement is true, nine is less than thirty-five. The answer is TRUE.
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