Absolute values can be interpreted as the distance away from a midpoint. To write the compound inequality, solve the absolute value inequality.
Absolute Value Inequality: |x-3600|≤ 4 Compound Inequality: 3596 ≤ x ≤ 3604
Practice makes perfect
Let's begin by writing 100 yd in terms of in. We can determine the conversion factor using the fact that 1 yd= 36 in.
Conversion Factor:
36in/yd
Next, we can multiply 100 yd by the conversion factor.
Now that the given measures have the same unit, we can create an absolute value inequality. Then, we can rewrite it as a compound inequality.
Absolute Value Inequality
Absolute values can be interpreted as the distance away from a midpoint. Because of this, we can write any absolute value inequality in the same general format. For the given case, the midpoint and the distance represent the length and the tolerance, respectively.
|x- midpoint| ≤ distance
⇕
|x- length| ≤ tolerance
We are given that the length is 3600 in. and the tolerance is 4 in. Let's substitute these values into the absolute value inequality.
|x- 3600| ≤ 4
Compound Inequality
The absolute value inequality says that x- 3600 is less than or equal to 4 "and" greater than or equal to -4.
x- 3600≤ 4 and x- 3600 ≥ -4
To write this as a compound inequality, let's first solve these inequalities.
Now, we will combine these solutions. To make this a bit easier, let's rewrite x ≥ 3604 as 3596≤ x.
Inequality I:& x ≤ 3604
Inequality II:& 3596 ≤ x
Compound:& 3596 ≤ x ≤ 3604
