Algebra Review

Solving for x

100

x + 14 = 30

16

200

3x - 5 = 10

5

300

x/4 + 2 = 10

32

400

3x + 8 = x + 12

2

500

x/-3 +7 = 2

15

Evaluating Expressions

100

x=5, find 3x+4

19

200

y=-2, find 4y+10

2

300

a=3, b=4, find a²+b

13

400

x=2, find 3(x+5) - 4

17

500

x=-3, y=4, find x² - 2y+5

6

Distributive Property

100

2(x + 3)

2x+6

200

-5(x-4)

-5x+20

300

-3(x+2)

-3x-6

400

4(2x-1) - 2(-3x-5)

14x + 6

500

-2(x-5) - 3(x+2)

-5x+4 

Word Problems

100

A taxi charges $5 plus $2 per km. Write the expression.

2x+5

200

A phone plan is $30 plus $0.05 per text. If the bill is $42.50, how many texts were sent?

$0.05x + 30 = 42.50 

x=250

300

A rectangle has a perimeter of 24. The length is x and width is 4. Find x.

x=8

400

The "Pizza Party" Showdown (Revised)

The Scenario: The Grade 8 class is ordering pizza for a celebration. They have a total budget of $90 and are comparing two local shops:

• Pizza Palace: Charges a flat delivery fee of $10, plus $12 per pizza.

• Dough Dash: Charges a flat delivery fee of $2, but $16 per pizza.

The Question: Using your algebra skills, calculate exactly how many whole pizzas the class can afford from each shop. Which shop gives them more food for their $90?

Shop 1: Pizza Palace

Equation: $12x + 10 = 90$

1. Subtract 10: $12x = 80$

2. Divide by 12: $x = 6.66...$

   Result: They can afford 6 whole pizzas.

Shop 2: Dough Dash

Equation: $16x + 2 = 90$

1. Subtract 2: $16x = 88$

2. Divide by 16: $x = 5.5$

   Result: They can afford 5 whole pizzas.

The Conclusion:

Even though Dough Dash has a much cheaper delivery fee ($2 vs. $10), the higher price per pizza means they can only buy 5. Pizza Palace is the better deal because they can get 6 pizzas and still have change left over!

500

The Scenario: Madame Whitehead is at the corner of a rectangular park that is 80 metres long and 60 metres wide. She needs to get to the opposite corner.

1. She can walk along the outside edge (the length then the width).

2. Or, she can take the diagonal shortcut across the grass.

The Question: How many metres does Madame save by taking the diagonal shortcut instead of walking along the edge?

40m

Boss Level

100

2(3x-2) +9 = -5x

x=-5/11

200

6y - 12 - 2y + 6 = 10

y=4

300

5a-2 = 9a +8

a=5/7

400

-2q -3 = -2(2q+1)

q=1/2

500

Solve for n: 4(n + 2) = 2(n - 6)

n= - 10