SOLUTION: Solve problem using an absolute value equation or inequality In 1985 Steve Cram set a world record of 3 minutes 29.67 seconds for the 1500 �meter race and a world record of 3 m

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Question 84957: Solve problem using an absolute value equation or inequality
In 1985 Steve Cram set a world record of 3 minutes 29.67 seconds for the 1500 �meter race and a world record of 3 minutes 46.31 seconds for the 1-mile race.
Suppose you know only that these two events occurred 11 days apart and that the 1500 meter record was set on July 16. Use an absolute value equation to find the possible dates for the 1-mile record run.

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
The key information that problem tells you is that the two races occurred 11 days apart and
that one of the races occurred on July 16. A little reasoning will tell you that the other
race (the mile event) was either 11 days earlier than July 16 or 11 days after July 16.
Therefore, you can deduce that the mile run was either on July 5 or on July 27.
.
But how do you write this in the form of an absolute value equation? Let D represent
the date on which the mile run occurred. Then you know that the difference between
D and 16 must equal 11. So you can write the absolute value equation as:
.

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You can solve this in the following manner. Write two separate equations, one using
the quantity in the absolute value signs with a + sign in front, and the other using the
same quantity in the absolute value signs with a - sign in front. Let's do these two equations,
one at a time.
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The quantity inside the absolute value signs is (D - 16). Put a + sign in front of this
quantity and the equation becomes:
.
+(D - 16) = 11
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You can just remove the parentheses and the equation then becomes:
.
D - 16 = 11
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Solve by adding +16 to both sides to get:
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D = 27
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So this tells you that July 27 is one solution.
.
Next solve the equation that results from putting a minus sign in front of the quantity
inside the absolute value sign.
.
-(D - 16) = 11
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To remove the parentheses you must change the sign of all the terms inside them. This is
caused by the minus sign in front of the parentheses. (You can look at it as a distributed
multiplication of -1 times the terms inside the parentheses.) When you remove the
parentheses the equation becomes:
.
-D + 16 = 11
.
Subtracting 16 from both sides of this equation results in:
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-D = -5
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And solve for +D by multiplying both sides of this equation by -1 to get:
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D = 5
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This tells you that the mile record might have also been set on July 5.
.
So now we have confirmed algebraically what we sort of figured logically at the start of
this problem ... the mile run was either on July 5 or July 27.
.
Hope this helps you to understand the problem a little better.
.