SELF Maths Difficulty: EASY

Algebra & Graphs 2.2

Equations

In this section, you will learn:

• Solving one-step linear equations
• Solving two-step linear equations
• Building equations from a worded scenario

Section 1: Concept-Builder
1. Solve one-step equations
a) 𝑥 + 3 = 9 b) 𝑥 − 7 = 1

𝑥
c) 2𝑥 = 18 d) =3
3

2. Solve two-step equations

𝑥
a) 2𝑥 + 1 = 5 b) +4 = 2
2

𝑥−5 𝑥+2
c) =3 d) −1 = 3
3 5

3. Jackson has 𝑥 toy cars. He bought 12 more, and now has a total of 28.
a) Write an expression for the number of toy cars he has in terms of 𝑥.

b) Write an equation using your answer in (a)

c) Solve this equation to find the number of cars Jackson has

Section 2: Tech-Free Questions
4. Solve one-step equations
a) 𝑥 + 2 = 5 b) 𝑥 − 3 = 2

c) 𝑥 − 4 = 6 d) 𝑥 − 10 = 3

e) 3 − 𝑥 = 5 f) 9−𝑥 =5

g) 2𝑥 = 6 h) 3𝑥 = −12

i) 4𝑥 = −20 j) −17𝑥 = 51

𝑥 𝑥
k) 2
=4 l) 3
=5

−𝑥 𝑥
m) 5
= 10 n) 3
= −18

3𝑥 5𝑥
o) 4
= 15 p) = 25
7

5. Solve two-step equations

a) 2𝑥 − 2 = 6 b) 3𝑥 + 3 = 6
c) 3 − 2𝑥 = 9 d) 4 + 3𝑥 = 40

𝑥 𝑥
e) +1 = 5 f) − 5 = 10
2 3

𝑥+4 2𝑥−4
g) 5
=2 h) =8
2

i) 2(𝑥 + 5) = 10 j) 3(𝑥 + 3) = 9

𝑥 𝑥
k) 2
− 4 = 10 l) 13 − 5 = 3

𝑥 𝑥+3
m) 10 − 2 = 4 n) − 5 = 10
2
 3−4𝑥 7−𝑥
o) =5 p) −2 = 2
3 4
Section 3: Tech-Free Application Questions
For each of the following, form equations from these worded questions. Then solve them.
6. I had some erasers, and sold 12 of them. I now have 6 left. How many did I start with?

a) Define your variable

𝐿𝑒𝑡 𝑥 𝑏𝑒 “___________________________”

b) Write the expression in terms of 𝑥

c) Use your answer in (b) to form an equation

d) Solve your equation in (c) to find out how many erasers he started with.

7. At a book sale, each book costs $1.60. If I have $8, how many books can I buy?

8. I have a pack of tissue; I used a quarter of them after my lunch. If I had used 3 pieces, how many were there in
packet originally?

9. Jack has some Pokémon trading cards. He buys 14 more, and then splits the new total between him and 3 other
friends. Each of them now has 6 trading cards. How many cards did he have to begin with?
10. I won the small prize money in the lottery. I spent half of it on a video game, and then gave $3 to my sister. If I now
have $6 left, how much did I win?

11. John usually eats x meals a day. On Monday he had sports so he ate an extra meal. If he had a total of 29 meals in
that week, how many meals does he have in a day?

12. I have a few 1-dollar coins. I used 4 of them on my lunch. I then changed the remainder into 2-dollar coins. If I ended
up with five 2-dollar coins, how many 1-dollar coins did I start with?

13. I own a car business. On the first day, the first batch of shipment came in. I managed to sell 3 cars. On the second
day, the next batch of shipment came in and it doubled the number of cars I had. I then sold 4 more cars. If I have 48
cars now, how many cars came in on the first day?
14. I have $20. I spent some of it on my lunch. I then spent half of the reminder on a cup of bubble tea, and another $3
on a piece of cake. If I have $1.50 left, how much did I spend on my lunch?

15. Jacob spends some time at work each day. If he spends his first 2 hours of work checking emails, and a quarter of
the reminding time talking to clients and still has to work for 6 hours, how many hours does he work in a day?
Section 4: Multiple Choice Exit Ticket
You have five minutes to complete these ten questions

1. 2𝑥 − 10 = 28

A. 𝑥 = 19 B. 𝑥 = 9 C. 𝑥 = 36 D. 𝑥 = −9 E. 𝑥 = −76

20−𝑎
2. 2
= −5

A. 𝑎 = 10 B. 𝑎 = 30 C. 𝑎 = −10 D. 𝑎 = 20 E. 𝑎 = −20

12𝑥
3. 15
− 2 = 8, 𝑥 =

A. 4.8 B. 8 C. 12.5 D. 7.5 E. 10

4. Mom put $𝑥 into a pool of money, and dad contribute $20 into the pool. They share the pool amongst their 4
children. Each child received $18. The equation to solve this would be:
𝑥 𝑥−20
A. 4𝑥 + 20 = 18 B. + 20 = 18 C. =4
4 18
𝑥+20 E. 18 − (𝑥 + 20) = 4
D. 18 = 4

5. Each pack of biscuits contains 𝑛 biscuits. Jason bought 3 packs, and ate 6 biscuits. He then gave half the remainder
to his sister. His sister received 5 biscuits. The equation to solve this problem would be:

3 3 1
A. 𝑛−6=5 B. (𝑛 − 6) = 5 C. 𝑛 −2=5
2 2 2
3(𝑛−6) 1
D. =5 E. (3𝑛 − 6) = 5
2 2

6. (9 − 𝑥) + 20 = 14 , then 𝑥 is

A. 2 B. 3 C. −3 D. 25 E. −25

7. Three less than a quarter of a number is 12. This can be written as

12−𝑥 𝑥−3 𝑥 𝑥+3

A. =3 B. = 12 C. + 3 = 12 D. = 12 E. None of these
4 4 3 4

8. A rectangle has a length 2metres longer than twice its width. Its perimeter is 22m. The width is:

A. 4m B. 5m C. 6m D. 2m E. 3m

9. Charlie usually works the same number of hours in a weekday. He does not work on Saturdays and Sundays. On
Monday he works 2 hours more than his usual, whereas on Friday he works half the time of his usual day. If he
works a total of 29 hours in a week, how many hours does he work on Monday?

A. 5 B. 6 C. 7 D. 8 E. 9

10. There is a straight railroad linking Pleasant Town with Joy City. A train leaves Pleasant Town at 9am, travels at
80km/h towards Joy City without stopping along the way. It stops at Joy City to drop off and pick up passengers for
half an hour. It then travels at 120km/h back to Joy City without stopping. It reaches Joy City again at 2.30pm. How
far apart is Pleasant Town and Joy City?
A. 180 km B. 240 km C. 300km D. 360 km E. None of these
ANSWERS:
Section 1:
1. a) 𝑥 = 6 b) 𝑥 = 8
c) 𝑥 = 9 d) 𝑥 = 9
2. a) 𝑥 = 2 b) 𝑥 = −4
c) 𝑥 = 14 d) 𝑥 = 18
3. a) 𝑥 + 12 b) 𝑥 + 12 = 28 c) 𝑥 = 16
Section 2:
4. a) 3 b) 5
c) 10 d) 13
e) -2 f) 4
g) 3 h) -4
i) -5 j) -3
k) 8 l) 15
m) -50 n) -54
o) 20 p) 35
5. a) 4 b) 1
c) -3 d) 12
e) 8 f) 45
g) 6 h) 10
i) 0 j) 0
k) 28 l) 50
m) 12 n) 27
o) -3 p) -9

Section 3:
6. a) the number of erasers b) 𝑥 − 12
c) 𝑥 − 12 = 6 d) 𝑥 = 18
7. 1.6𝑥 = 8; 𝑥 = 5
1
8. 𝑥 = 3; 𝑥 = 12
4
𝑥+14
9. 4
= 6; 𝑥 = 10
𝑥
10. 2
− 3 = 6; 𝑥 = 18
11. 7𝑥 + 1 = 29; 𝑥 = 4
𝑥−4
12. 2
= 5; 𝑥 = 14
13. 2(𝑥 − 3) − 4 = 48; 𝑥 = 29
20−𝑥
14. − 3 = 1.5; 𝑥 = 11
2
3(𝑥−2)
15. 4
= 6; 𝑥 = 10
Section 4:
1. A 2. B 3. C 4. D 5. E
6. B 7. E 8. E 9. B 10. E