Inequalities — Practice

Some questions have a whole range of answers, and a number line is how you show them all.

What these questions cover

These questions use 1 idea from the course. Follow any of them for a definition, where it is taught, and what it leads to.

Problem 1

Which symbol means "at least"?

  1. ≥
  2. >
  3. ≤
  4. <
Worked answer

≥

"At least" includes the value itself

Problem 2

Which symbol means "fewer than"?

  1. <
  2. ≤
  3. >
  4. ≥
Worked answer

<

Strictly less

Problem 3

Write "you must be at least 13 to join" using a for age. Use >= for the symbol.

Worked answer

a>=13

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Problem 4

Write "no more than 20 people" using p. Use <= for the symbol.

Worked answer

p<=20

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Problem 5

For x < 7, is the circle at 7 open or filled?

  1. Open
  2. Filled
  3. Either
  4. There is no circle
Worked answer

Open

7 < 7 is false, so 7 is excluded

Problem 6

Solve x + 4 < 11. Give the answer as x<number.

Worked answer

x<7

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Problem 7

Solve x - 3 ≥ 5. Give the answer as x>=number.

Worked answer

x>=8

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Problem 8

Solve 5x ≤ 40. Give the answer as x<=number.

Worked answer

x<=8

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Problem 9

Does "over 21" include 21?

  1. No
  2. Yes
  3. Sometimes
  4. Cannot tell
Worked answer

No

It means > 21, so 21 is excluded

Problem 10

Which value satisfies x ≥ -2?

  1. -1
  2. -5
  3. -3
  4. -10
Worked answer

-1

-1 ≥ -2 is true

Problem 11

How many whole numbers satisfy 1 ≤ n ≤ 6?

Worked answer

6

1,2,3,4,5,6

Problem 12

Tickets cost $7 and you have $50. How many can you buy?

Worked answer

7

n ≤ 7.14

Tickets are whole, so 7

Problem 13

A lift holds at most 600 kg. If each person is 75 kg, how many can ride?

Worked answer

8

n ≤ 8

Problem 14

A taxi charges $3 plus $2 a mile. With $20, how many whole miles can you go?

Worked answer

8

2m ≤ 17

m ≤ 8.5, so 8 whole miles

Problem 15

How many whole numbers satisfy -3 < n < 4?

Worked answer

6

-2,-1,0,1,2,3

Problem 16

Which phrase matches x ≤ 10?

  1. At most 10
  2. More than 10
  3. At least 10
  4. Fewer than 10
Worked answer

At most 10

"At most" is ≤

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