Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A meteorologist is tracking the daily high temperatures in a desert region. The temperature T (in degrees Celsius) for a particular day is given by the expression 5x - 8, where x represents the number of hours past sunrise. If the temperature on this day ranged from 12°C to 27°C, which inequality represents the possible values for x?
- A20 ≤ x ≤ 35
- B4 ≤ x ≤ 7
- C5 ≤ x ≤ 8
- D12 ≤ x ≤ 27
Show answer & explanationAnswer & explanation
Correct answer: B. 4 ≤ x ≤ 7
The temperature T is given by 5x - 8. The range of temperatures is 12°C to 27°C. So, we set up the inequality: 12 ≤ 5x - 8 ≤ 27. First, add 8 to all parts of the inequality: 12 + 8 ≤ 5x - 8 + 8 ≤ 27 + 8, which simplifies to 20 ≤ 5x ≤ 35. Next, divide all parts by 5: 20/5 ≤ 5x/5 ≤ 35/5, which simplifies to 4 ≤ x ≤ 7. This means x, the number of hours past sunrise, ranges from 4 to 7.
Why the other options are wrong
- A. This is the range for 5x, before subtracting 8 and dividing by 5.
- C. This might come from misinterpreting parts of the expression or incorrect algebraic manipulation.
- D. This represents the given temperature range, not the range for x.
Solving Compound Inequalities
A compound inequality combines two or more inequalities. To solve it, apply inverse operations to all parts (left, middle, right) simultaneously to isolate the variable in the middle.
- Operations must be applied to all three parts of the inequality.
- Multiplying or dividing by a negative number reverses the inequality signs.
- The goal is to isolate the variable in the middle.
Memory trick: Balance the middle, move to all sides, then divide!