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Absolute value answers the question of "how far," and not "which way." The phrase "how far" implies "length" and length is always a nonnegative quantity . Thus, the absolute value of a number is a nonnegative number.
Determine each value.
. The quantity on the left side of the equal sign is read as "negative the absolute value of 5." The absolute value of 5 is 5. Hence, negative the absolute value of 5 is -5.
. The quantity on the left side of the equal sign is read as "negative the absolute value of -3." The absolute value of -3 is 3. Hence, negative the absolute value of -3 is .
By reasoning geometrically, determine each absolute value.
From the problems in [link] , we can suggest the following algebraic definition of absolute value. Note that the definition has two parts.
The algebraic definition takes into account the fact that the number could be either positive or zero or negative .
Use the algebraic definition of absolute value to find the following values.
. The number enclosed within the absolute value bars is a nonnegative number, so the upper part of the definition applies. This part says that the absolute value of 8 is 8 itself.
. The number enclosed within absolute value bars is a negative number, so the lower part of the definition applies. This part says that the absolute value of -3 is the opposite of -3, which is . By the definition of absolute value and the double-negative property,
Use the algebraic definition of absolute value to find the following values.
Determine each of the values.
A Mission Control Officer at Cape Canaveral makes the statement “lift-off, T minus 50 seconds.” How long is it before lift-off?
Due to a slowdown in the industry, a Silicon Valley computer company finds itself in debt $2,400,000. Use absolute value notation to describe this company’s debt.
A particular machine is set correctly if upon action its meter reads 0. One particular machine has a meter reading of upon action. How far is this machine off its correct setting?
( [link] ) Find the value of .
( [link] ) The ratio of acid to water in a solution is . How many mL of acid are there in a solution that contain 112 mL of water?
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