Solving Linear Equations: Every Type in the Exam — Worksheet & Memo

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FREE CAPS MATHS RESOURCES

Grade 9 · Equations

Solving Linear Equations: Every Type in the Exam

MARKING GUIDELINE

Marks

Duration

45 minutes

Questions

Name:

Class:

Date:

Mark

/ 30

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
Solve for x: 3x − 7 = 14
(1)
A)2,33
B)7✓
C)21
D)−7
Answer: B — 3x = 21, so x = 7.
- A — divided 14 by 3 before adding 7
- C — forgot to divide by 3
- D — moved the 7 without changing its sign
1.2
Solve for x: 2(x + 3) = 16
(1)
A)11
B)5✓
C)8
D)13
Answer: B — x + 3 = 8, so x = 5.
- A — did not divide by 2 first
- C — forgot to subtract the 3
- D — divided 16 by 2 and added 5
1.3
Solve for x: 5x − 3 = 2x + 12
(1)
A)3
B)5✓
C)15
D)1,8
Answer: B — 3x = 15, so x = 5.
- A — divided 9 by 3
- C — forgot to divide by 3
- D — divided before collecting the terms
1.4
Solve for x: x4 = 6
(1)
A)1,5
B)24✓
C)10
D)2
Answer: B — Multiply both sides by 4.
- A — divided instead of multiplying
- C — added 4
- D — subtracted 4
1.5
Solve for x: −2x = 10
(1)
A)5
B)−5✓
C)−20
D)8
Answer: B — Dividing by −2 gives −5.
- A — lost the negative sign
- C — multiplied instead of dividing
- D — subtracted 2 from 10
1.6
When a term is moved across the equals sign, its …
(1)
A)value doubles
B)SIGN changes✓
C)value halves
D)sign stays the same
Answer: B — Moving a term is really doing the inverse operation to both sides.
- A — nothing is doubled
- C — nothing is halved
- D — if the sign stayed the same, the equation would change
1.7
Three consecutive integers add up to 39. The SMALLEST is …
(1)
A)12✓
B)13
C)11
D)39
Answer: A — x + (x+1) + (x+2) = 39 gives 3x = 36, so x = 12.
- B — that is the MIDDLE integer
- C — 11 + 12 + 13 = 36, not 39
- D — that is the total, not one of the integers
1.8
Solve for x: 2x + 13 = 5
(1)
A)7✓
B)8
C)2
D)16
Answer: A — 2x + 1 = 15, so 2x = 14 and x = 7.
- B — forgot to subtract the 1 before halving
- C — divided 5 by 2 and ignored the 3
- D — ADDED the 1 instead of subtracting it
1.9
A number is doubled and 7 is added, giving 31. The number is …
(1)
A)19
B)12✓
C)24
D)38
Answer: B — 2x + 7 = 31, so 2x = 24 and x = 12.
- A — subtracted 7 but did not halve
- C — that is 2x, not x
- D — doubled 19
1.10
If 4x = 0, then x = …
(1)
A)4
B)0✓
C)undefined
D)−4
Answer: B — The only number that gives 0 when multiplied by 4 is 0.
- A — 4 × 4 = 16
- C — the equation has a perfectly good solution
- D — −4 × 4 = −16

Answer grid — marking guideline

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[10 MARKS]

Solve for x. Show ALL your steps.

2.1
6x − 5 = 2x + 11
(3)
6x − 2x = 11 + 5 (1)
4x = 16 (1)
x = 4 (1)
2.2
5(x − 3) = 2(x + 3)
(4)
5x − 15 = 2x + 6 (2)
3x = 21 (1)
x = 7 (1)
2.3
10 − 3x = 1
(3)
−3x = 1 − 10 (1)
−3x = −9 (1)
x = 3 (1)

Question 3

[10 MARKS]

Solve for x, and then answer the word problem.

3.1
x3 + 2 = 5
(3)
x3 = 3 (1)
x = 3 × 3 (1)
x = 9 (1)
3.2
12 − 5x = 2x − 2
(3)
12 + 2 = 2x + 5x (1)
14 = 7x (1)
x = 2 (1)
3.3
The sum of three consecutive whole numbers is 51. Set up an equation and determine the three numbers.
(4)
Let the numbers be x, x + 1 and x + 2 (1)
x + (x + 1) + (x + 2) = 51 (1)
3x + 3 = 51, so x = 16 (1)
16, 17 and 18 (1)

TOTAL: 30 marks

This question paper consists of 3 questions.