Question

Engage

1. absolute value: the distance a number is from zero (always positive)

2. inequalities: >(greater than) or < (less than)

3. negative numbers: numbers that are on the left side of zero (the closer to zero a negative number is, the greater the number is in value) ex. -3>-5

Answer 1

Nice — here’s a short, clear summary and some quick practice so you can engage with the ideas.

Key ideas
- Absolute value: |x| = distance from x to 0, always nonnegative. Examples: |3| = 3, |-3| = 3, |0| = 0.
- Inequalities: ">" means greater than (to the right on the number line), "<" means less than (to the left). Example: 5 > 2.
- Negative numbers: numbers less than 0. The closer a negative is to 0, the larger its value. Example: -3 > -5 because -3 is closer to 0.

Important rule with inequalities:
- Adding or subtracting the same number keeps the inequality direction.
- Multiplying or dividing by a negative number flips the inequality sign. (e.g., if -2x > 6, dividing by -2 gives x < -3)

Practice (with answers)
1. Which is greater: -3 or -5?
- Answer: -3 > -5 (because -3 is closer to 0).

2. Compare absolute values: |−7| and |4|.
- Answer: |−7| = 7, |4| = 4, so |−7| > |4|.

3. Solve: 2x + 3 > 7.
- Work: 2x > 4 → x > 2.

4. Solve: −3x < 9.
- Work: divide by −3 (flip sign) → x > −3.

5. Order least to greatest: −2, −8, 0, 3.
- Answer: −8, −2, 0, 3.

6. True or false: |−2| < |−5|?
- Answer: True (2 < 5).

Want more problems, visual number-line sketches, or explanations of a specific step?