Solving Multi-Step Equations & Inequalities

Solving by Combining Like Terms

100

5h + 2 + 2h = 23

h = 3

200

How old was Mrs Christl when she got married?

23

300

3a + 12 - 6a = -9

a = 7

400

What language does Mrs Christl grow up speaking?

Cantonese

500

78 = 3c + 12 - c + 4

c = 31

Solving by Using the Distributive Property

100

2(x + 5) = 14

x = 2

200

7(4 - t) = -84

t = 16

300

What year did Mrs Christl come to Australia?

2016

400

-2(x - 9) + 3 (x-2) = -24

-2(x - 9) + 3 (x-2) = -24

-2x +18 + 3x - 6 = -24

                x +12 = -24

                       x = -36

500

Solve and simplify 

-13(4 + 2a) = 2(2a+1)-5

-13(4 + 2a) = 2(2a+1)-5

      -52-26a = 4a+2-5

           -22a =49

                a = -49/22

Inequalities & Factorising

100

Solve. 6p - 18 -2p ≤ -2

p ≤ 4

200

Solve. 3 - 5(a + 4) ≥ -a + 7

a ≤ -4

300

Factorise 3xy - 6x

3x(y-2)

400

Factorise 6a²b³ - 2ab

2ab (3ab² -1)

500

4/5(15x + 45) ≥ -6x

x ≥ -2

Others

100

Simplify 2ab + 3b² - 3ab - b²

2ab + 3b² - 3ab - b²

= -ab + 2b²

200

Expand and simplify where possible

2(x-2)-2(xy-3)

2y(x-2)-2(xy-3)

= 2xy-4y-2xy+6

= -4y+6 OR 6-4y

300

Use Index Laws simplify the following

2a²b³ x 8ab

16a³b⁴

400

Use Index Laws simplify the following

6a⁰ + 2a³ x 4a²b

6+ 8a⁵b

500

Use Index Laws simplify the following

(2ab x 2b)⁰ + 2a

 2a

Word Problems

100

WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?

n - Julie's sister's age n + 3 = 11 n = 8 Julie's sister is 8 years old.

200

Bella earns $15 per hour on the weekends babysitting. She also charges an extra $5 for travel. How many hours will she need to babysit to earn $155?

Let x be the number of hours she will need to babysit. 

15x + 5 = 155

x = 10 hours 

300

Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?

Let be = the number of apples in each box.

4b-3 = 28

4b = 112

b = 28

400

The length of a rectangle is 4 times greater than its width. If the perimeter of the rectange is 40cm². What is the width and length of the rectangle, respectively?

Let w be the width.

2w + 2(4w) = 40

10w = 40

w = 4

Therefore, the width is 4cm, and the length is 16cm.

500

Dylan has $100. He wants to buy a book for $20 and some CDs for $15 each. At most, how many CDs can Dylan buy?

C = 5 (Interpret the quotient)