Grade 7 Equations: Inequalities

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   What is the greatest integer that makes −6x − 6 > 33 true?

   1. Add 6 to both sides: −6x > 39.
   2. Divide both sides by −6. Dividing by a negative number flips the sign (> becomes <): x < −6 1/2.
   3. The greatest integer less than −6 1/2 is −7.

   Answer: −7

2. Example 2

   An elevator can carry at most 1000 pounds. A worker who weighs 209 pounds is loading boxes that weigh 25 pounds each. What is the greatest number of boxes the worker can take up in one trip?

   1. Write the story as an inequality: 209 + 25b ≤ 1000.
   2. Subtract 209 from both sides: 25b ≤ 791.
   3. Divide both sides by 25: b ≤ 31 16/25.
   4. The greatest whole number less than or equal to 31 16/25 is 31.

   Answer: 31

3. Example 3

   What is the least integer that makes −4x + 5 ≤ −8 true?

   1. Subtract 5 from both sides: −4x ≤ −13.
   2. Divide both sides by −4. Dividing by a negative number flips the sign (≤ becomes ≥): x ≥ 3 1/4.
   3. The least integer greater than or equal to 3 1/4 is 4.

   Answer: 4