SELF STUDY GUIDE FOR GRADE 02/SMART TERM 02/2020
CHAPTER 09: EQUATIONS AND INEQUALITIES
I.
Solve the following linear equations
1. 𝑥 + 14 = 35
Answers: 1. 𝑥 = 21 2. 𝑦 = 6
3. 𝑞 = 8 4. 𝑚 = 4
5. 𝑑 = 8
2. 4𝑦 − 3 = 21
3. 5𝑞 = 4𝑞 + 8
4. 4(𝑚 − 6) = −8
5. 2(2𝑑 − 1) = 3(𝑑 + 2)
Answers: 1) 2
II.
2) 5
3) 5
4)4
Construct an equation and solve the equation.
1. I think of a number, add 2 and multiply this by 3. The answer is 12. What is the number?
2. I put the same number of chocolate buttons on each of seven cakes.
I had 40 buttons at the start and now have five buttons left over.
How many buttons did I put on each cake?
3. A number is subtracted from 7. The results multiplied by 3 and the answer is 6. What is the
number.
4. 9 times a number has 1 subtracted from it. The result is trebled.
The answer is same if you add 7 to twice the number and multiply the result by 7. What is
the number?
III.
Solve each pair of simultaneous equations by elimination.
1. 𝑚 + 𝑛 = 7
5. 2𝑙 − 𝑚 = −1
Answers:
4𝑚 − 𝑛 = 23
2𝑙 + 3𝑚 = 11
1. 𝑚 = 6, 𝑛 = 1
2. 𝑒 + 𝑓 = 5
4𝑒 − 𝑓 = 5
3. 3𝑝 + 2𝑞 = 14
5𝑝 − 2𝑞 = 2
4. 𝑔 + ℎ = 3
𝑔 + 3ℎ = 7
2. 𝑒 = 2, 𝑓 = 3
6. 3𝑟 − 𝑠 = −1
3𝑟 − 2𝑠 = −8
Answers:
5. 𝑙 = 1, 𝑚 = 3
6. 𝑟 = 2, 𝑠 = 7
3. 𝑝 = 2, 𝑞 = 4
7. 𝑟 + 2𝑠 = 0
3𝑟 − 𝑠 = −7
7. 𝑟 = −2, 𝑠 = 1
4. 𝑔 = 1, ℎ = 2
8. 3𝑚 − 4𝑛 = −14
2𝑚 + 2𝑛 = 14
8. 𝑚 = 2, 𝑛 = 5
9. The sum of two number is 12, and their difference is 8. Form two equations and solve them
to find the two numbers.
IV.
Write the inequalities in words.
1. 𝑥 ≥ 6
2. 𝑦 < 5
3. 3 < 𝑒 ≤ 6
4. 4 > 𝑗 ≥ 0
V.
Show each of these inequalities on a number line.
1. 𝑚 ≥ −1
2. 7 < 𝑓
3. 5 ≥ 𝑟 ≥ 2
4. −2 ≤ 𝑖 < 2
5. 5 ≥ ℎ > −4
VI.
Write the inequality shown by each of the following number lines, using the given letter for the
unknown.
1. 𝑎
2. 𝑏
3. 𝑐
VII.
Solve the following inequalities
1. 𝑥 + 3 > 2
2. 3𝑥 + 2 > 5
3. 6𝑥 + 4 ≥ 5𝑥
4. 3𝑦 − 4 < 5𝑦 + 2
Answers:
1) 𝑥 > −1
2) 𝑥 > 1
3) 𝑥 ≥ −4
4) 𝑦 > −3
5) 1 < 𝑥 ≤ 6
5. 3 < 𝑥 + 2 ≤ 6
6. 8 < 2(𝑥 − 4) ≤ 10
7. 6 ≥ 2(𝑥 + 1) > 12
6) 8 < 𝑥 ≤ 9
7) 2 > 𝑥 > 5