1. 1.1

   Solve for x: 3x − 5 > 7

   (1)
   A)x < 4

   B)x > 2

   C)x ≥ 4

   D)x > 4✓
   Answer: D — 3x > 12, so x > 4.

   • A — the sign reverses only when you divide by a NEGATIVE, and 3 is positive
   • B — worked out 7 − 5 = 2 and ignored the 3 — the 5 must be ADDED, and 3x still divided by 3
   • C — the sign is >, so 4 itself is NOT included
2. 1.2

   Solve for x: −2x > 6

   (1)
   A)x > −3

   B)x > 3

   C)x < 3

   D)x < −3✓
   Answer: D — Dividing both sides by −2 REVERSES the inequality sign.

   • A — did not reverse the sign when dividing by a negative
   • B — lost the negative AND kept the sign the same way round
   • C — divided 6 by 2 and lost the negative
3. 1.3

   Write x ≥ −2 in interval notation.

   (1)
   A)[−2 ; ∞)✓

   B)(−∞ ; −2]

   C)[−2 ; ∞]

   D)(−2 ; ∞)
   Answer: A — A square bracket includes −2, and infinity always takes a round bracket.

   • B — that is x ≤ −2, the other direction
   • C — infinity is never reached, so it never takes a square bracket
   • D — a round bracket EXCLUDES −2, but ≥ includes it
4. 1.4

   Solve for x: −1 ≤ 2x − 1 < 5

   (1)
   A)0 < x ≤ 3

   B)0 ≤ x < 3✓

   C)−1 ≤ x < 5

   D)−2 ≤ x < 4
   Answer: B — Add 1 throughout to get 0 ≤ 2x < 6, then divide throughout by 2.

   • A — swapped the two inequality signs on the way through
   • C — never divided by the 2 at all
   • D — SUBTRACTED 1 throughout instead of adding it, and never divided by 2
5. 1.5

   List the integers satisfying −2 < x ≤ 3.

   (1)
   A)−1 ; 0 ; 1 ; 2 ; 3✓

   B)−2 ; −1 ; 0 ; 1 ; 2 ; 3

   C)−2 ; −1 ; 0 ; 1 ; 2

   D)−1 ; 0 ; 1 ; 2
   Answer: A — The < sign excludes −2, and the ≤ sign includes 3.

   • B — included −2, but < excludes it
   • C — read BOTH signs the wrong way round
   • D — left out 3, but ≤ includes it
6. 1.6

   Solve for x: x/3 + 1 < 4

   (1)
   A)x < 11

   B)x < 3

   C)x < 12

   D)x < 9✓
   Answer: D — Subtract 1 to get x/3 < 3, then multiply both sides by 3.

   • A — multiplied through by 3 but tripled only the x, not the 1
   • B — subtracted the 1 but never multiplied by 3
   • C — forgot to subtract the 1 before multiplying by 3
7. 1.7

   A taxi charges R12 plus R7 per kilometre. For the fare to stay UNDER R75, the trip must be …

   (1)
   A)more than 9 km

   B)less than 9 km✓

   C)less than 10,71 km

   D)less than 63 km
   Answer: B — 12 + 7d < 75 gives 7d < 63, so d < 9.

   • A — reversed the inequality — a SHORTER trip is the cheaper one
   • C — divided 75 by 7 without first subtracting the R12 flag fall
   • D — forgot to divide the 63 by the R7 per kilometre
8. 1.8

   Solve for x: 5 − x ≥ 2

   (1)
   A)x ≤ 3✓

   B)x ≥ −3

   C)x ≥ 3

   D)x ≤ 7
   Answer: A — −x ≥ −3, and multiplying by −1 reverses the sign to give x ≤ 3.

   • B — kept the −3 and did not reverse the sign either
   • C — did not reverse the sign when multiplying by −1
   • D — added the 2 to the 5 instead of subtracting it
9. 1.9

   The interval (2 ; 7] means …

   (1)
   A)x > 2 and x < 7

   B)x ≥ 2 and x < 7

   C)x > 2 and x ≤ 7✓

   D)x ≥ 2 and x ≤ 7
   Answer: C — A round bracket excludes the 2; a square bracket includes the 7.

   • A — the square bracket at 7 INCLUDES it
   • B — the two brackets have been read the wrong way round
   • D — the round bracket at 2 EXCLUDES it
10. 1.10

    Solve for x: 4(x − 1) ≤ 2x + 6

    (1)
    A)x ≥ 5

    B)x ≤ 3,5

    C)x ≤ 5✓

    D)x ≤ 10
    Answer: C — 4x − 4 ≤ 2x + 6 gives 2x ≤ 10, so x ≤ 5.

    • A — the sign reverses only when dividing by a NEGATIVE, and 2 is positive
    • B — multiplied only the x by 4, leaving the −1 inside untouched
    • D — forgot to divide the 10 by the 2

This question paper consists of 3 questions.