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Understanding and using absolute value
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The absolute value of a number is its distance from zero on the number line.
Symbol:
Key point: Distance is always positive (or zero)!
Find:
The absolute value is the distance from zero.
is 12 units from zero.
Avoid these 3 frequent errors
See how this math is used in the real world
Solve .
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Numbers like 5 and -5 are opposites (same absolute value, different signs).
If and , then
Evaluate inside first, then take absolute value:
To compare and :
Answer:
Find:
The absolute value is the distance from zero.
is 12 units from zero.
Answer:
Evaluate:
Step 1: Evaluate inside the absolute value bars
Step 2: Take absolute value
Answer:
Evaluate:
Step 1: Evaluate inside the absolute value bars
Step 2: Take absolute value
Answer:
Evaluate:
Step 1: Evaluate each absolute value
For :
Step 2: Subtract
Answer:
Evaluate:
Step 1: Evaluate each absolute value
For :
Step 2: Subtract
Answer:
Evaluate: |7 - 10|
Step 1: Evaluate inside the absolute value first. 7 - 10 = -3
Step 2: Find the absolute value. |-3| = 3
Remember: Always do operations inside the bars first, then take absolute value.
Answer: 3
Solve for x: |x - 4| = 9
Step 1: Understand what this means. The distance between x and 4 is 9 units.
Step 2: Set up two equations. Case 1: x - 4 = 9 x = 13
Case 2: x - 4 = -9 x = -5
Step 3: Check both solutions. |13 - 4| = |9| = 9 ✓ |-5 - 4| = |-9| = 9 ✓
Answer: x = 13 or x = -5