Monomials and Binomials
Determine the sum or difference
3x + (−8x)
–5x
Evaluate 4x - 2 when x = 5.
18
Solve for the variable...
7.5x – 2.5x = 56.8 + 13.2
x = 14
Is x = 5 part of the solution for each inequality?
7x < –4 + 3x
No, x = 5 is not part of the solution.
An after-school program will offer a coding class next year if at least 15 students sign up. So far, 9 students have signed up.
Let s represent how many more students need to sign up. Which inequality describes the problem?
9 + s > 15
s + 9 ≥ 15
s + 9 ≥ 15
Determine the sum or difference
7x − 2 + 4x + 2
11x
Evaluate -3m + 4 when m = 6
-14
Solve for the variable
3x – (–6) = –15
x = –7
Is x = 5 part of the solution for each inequality?
–2x + 5x ≤ 8 + 13
Yes, x = 5 is part of the solution.
When Sabrina’s phone is fully charged, it can operate for at most 18 h before running out of battery power. It has been 6 h since Sabrina’s phone was fully charged.
Let p represent how many more hours Sabrina’s phone can operate without running out of battery power. Which equation or inequality describes the problem?
6 + p > 18
6 + p ≤ 18
p + 6 ≥ 18
6 + p ≤ 18
Determine the sum or difference
(2a + 4c) + (3a − 12c)
5a – 8c
Evaluate 2.5a + 1.5b when a = 4 and b = 2.
10 + 3 = 13
5.2x + 8.4 = –43.6
x = –10
Solve the inequality
–6 – 2 ≤ –3x + 4x
x ≥ –8.
A local community centre in Toronto charges a flat fee of $50 to rent a room for a birthday party, plus $15 per guest for snacks. If Sarah has a total budget of $260, write and solve an inequality to find the maximum number of guests (g) she can invite without going over her budget.
The total cost must be less than or equal to Sarah's budget:
Step 1: Subtract the flat fee ($50) from both sides:
Step 2: Divide both sides by the cost per guest ($15):
Sarah can invite a maximum of 14 guests.
Write the perimeter of a rectangle as a sum of binomials when the length is 3 times the width (w).
3w + w + 3w + w = 8w
The formula for the perimeter of a rectangle is P = 2l + 2w. Evaluate the perimeter if l = 5.5 and w = 3.5
11 + 7 = 18
4x – 3 = 15 – 2x
x = 3
Solve the inequality
–5s – 13 < –2s + 11
s > –8.
A local charity is washing cars to raise money. They spent $35 on soap and sponges. They charge $8 per car. Write and solve an inequality to find the minimum number of cars (c) they must wash to make a profit of more than $125.
8c - 35 > 125
8c > 160
c > 20.
They must wash 21 cars (since it must be more than 20 to make more than $125).
Simplify the expression: (8x - 5y) - (-3x + 2y)
8x - 5y + 3x - 2y
11x - 7y
Evaluate (-2x + 4y) - (3x - 2y) when x = 2 and y = 3.
-2x + 4y - 3x + 2y
-5x + 6y
-5(2) + 6(3)
-10 + 18 = 8
A Grade 8 class has a budget of $250 to organize an end of year celebration for the whole school. They spend $170 on snacks. The rest they will spend equally on arts & crafts supplies and prizes. How much money can they spend on each of these 2 items?
Write an equation to represent the scenario.
2m + 170 = 250
2m = 80
m = 40
Solve the inequality and state whether the graph would have an open or closed circle: -4x + 12 > 36
Subtract 12 from each side: -4x > 24
Divide by -4 and FLIP THE SIGN. x < -6
The graph has a closed circle.
A student council has $2000 in their bank account for community outreach. Every week, they withdraw $55 to donate to the local community center's homework club to pay for supplies. They do not make any deposits to their account or other withdrawals. How many weeks can the club withdraw money if they want to maintain a balance of at least $500? Use the following expression to determine the number of weeks the student council can make this withdrawal.
2000 – 55w ≥ 500
w is ≥ 27.27