This and That
Distribute
3(4x + 2)
What is:
12x + 6
Solving Equations
Solve for x.
x + 3 = 7
What is:
x = 4
Solving Inequalities
Solve for c.
c - 11 > 22
What is:
c < 33
Claire jogs around an oval track and is able to complete one lap in 5 minutes. If she jogs at the same pace for 42 minutes, how many laps would she be able to jog? Write an inequality and find the number of whole laps Claire completes.
x = number of laps Claire jogs
5x less than or equal to 42
x is less than or equal to 8.4
Claire is able to jog 8 whole laps.
After students borrowed 28 novels from the school library, there were 35 novels left. How many novels were in the school library at first?
63 novels
Solving Equations
Solve for x.
2x = 8
What is:
x = 4
What are two possible solutions for x?
2x < 4
x: 0,1, etc.
Write an algebraic equation to represent this scenario and solve:
When a number is tripled and 8 is subtracted from the result, the answer is 16. What is the number?
3x - 8 = 16
x = 8
When a number is doubled, the result is 48. What is the number?
24
Solving Equations
Solve for x.
5x = 25
What is:
x = 5
Write an inequality
S is at most 55
s <= 55
Write an algebraic equation to represent this scenario and solve.
Jason's age is 3 times Shauna's present age. in 4 years' time, the sum of their ages will be 56 years. Find their present ages.
x = Shauna's present age
(x+4) + (3x +4) = 56
Shauna = 12 y.o
Jason = 36 y.o.
Distribute and combine like terms:
4(3x + 5) - 2x + 15 = 10
12x + 20 - 2x + 15 = 10
10x +35 = 10
10x = -25
Solve for v.
v + 14 = 30
v = 16
Write an Inequality
J is less than 8
J < 8
Write an algebraic inequality to represent this scenario and solve.
For every 15 students on a field trip, there needs to be one teacher. How many teachers are needed for a group of 100 students?
y = number of teachers needed
15y greater than or equal to 100
y is greater than or equal to 6 2/3
7 teachers are needed.
Factor
3x + 6
What is:
3(x + 2)
Modeling Equations
Create an equation that represents the following expression and then solve it.
Harvey's age doubled is 6
2a = 6
a = 3
Modeling and Solving Inequalities
Create an inequality to represent the scenario and solve the inequality
Julie earns $7 for each car she washes. This week, she wants to save more than $56. How many cars must she wash?
What is:
7c > 56
Write an equation to represent this scenario and solve.
Jared has some quarters and dimes that total $5.50. If he has 8 more quarters than dimes, how many dimes does Jared have?
x = number of dimes Jared has
0.1y + 0.25(y + 8) = 5.50
y = 10
Jared has 10 dimes.