Equations
Solve: 6x + 1.6 = 58
6x = 56.4
x = 9.4
Haley solves the inequality 13 ≥ -r - 7 and graphs the solution on a number line with a solid circle at -20 and an arrow pointing left. Is she correct? Support your answer, and give the correct description if she is incorrect.
No, it should be a solid circle at -20 with an arrow pointing right. (she forgot to switch the direction of the inequality)
Solve and check: -15a + 32 = 167
-15a = 135
a=-9
(check by substituting back into the orginal equation)
Diego’s neighbors paid him to take care of their fish when they went on vacation. He spent $13 of his earnings on a book and $9 on some art supplies. Afterward, he had at most $10 left. Write an inequality to represent how much Diego’s neighbors paid him. Then solve the inequality.
x - 13 - 9 ≤ 10
x - 22 ≤ 10
x ≤ $32
Ms. Poppleton's favourite fruit
Raspberries
Solve: -8(0.5y - 3) = 3
-4y + 24 = 3
-4y = -21
y = 5.25
Solve and graph: 3 - 4t ≤ 39.5
- 4t ≤ 36.5
t ≥ -9.125
(closed circle to the right)
Solve. 6p - 18 -2p ≤ -2
Then check your solution.
p ≤ 4
6(4) - 18 -2(4) ≤ -2
24 - 18 - 8 ≤ -2
6 - 8 ≤ -2
-2 ≤ -2
In one month, Jason earns $32.50 less than twice the amount Kevin earns. Jason earns $212.50. How much does Kevin earn?
2k - 32.50 = 212.50
2k = 245
k =$122.50
Where Ms. Poppleton is going for winter break
Nowhere, I'm staying home
Solve: 4/5(25x + 7) = 37.6
20x + 5.6 = 37.6
20x = 32
x = 1.6
2(2.1z + 4.5) ≥ 21.6
4.2z + 9 ≥ 21.6
4.2z ≥ 12.6
z ≥ 3
Solve. 2(6x - 5) < 14
Then check your solution.
x < 2
2(6(2)-5)<14
2(12-5)<14
2(7)<14
14<14
Amelia can spend no more than $89 to rent a car for a day trip. A rental car costs $35 per day plus $0.20 per mile. Write and solve an inequality to find the possible distance in miles, m, that Amelia can drive without exceeding her budget.
35 + 0.2x ≤ 89
0.2x ≤ 54
x ≤270 miles
The names of Ms. Poppleton's siblings
Laura & James
Solve: 0.75(3n - 4) = 5.5n + 10
2.25n - 3 = 5.5n + 10
-13 = 3.25n
-4 = n
Solve. -4 (5x - 2) ≥ 4x + 5
Then graph your solution
1/8 or .125
Solve and check: -4(-6 - c) = -4
24 + 4c = -4
4c = -28
c= -7
The ticket price for a concert at a historic music hall includes $6.40 for the concert, $4.80 for the program, and a hall restoration fee. The price for 11 tickets is $128.15.
11(6.4 + 4.8 + x) = 128.15
11(11.2 +x) = 128.15
123.2 + 11x = 128.15
11x = 4.95
x = $0.45
Ms. Poppleton's least favourite food
Olives
-6x - 4(2x - 19) = 8(52) + 58
-6x - 8x + 76 = 8(25) + 58
-14x + 76 = 200 + 58
-14x + 76 = 258
-14x = 182
x= -13
4/5(15x + 45) ≥ -6x
x ≥ -2
The length of a rectangle is 3 inches longer than its width. The perimeter of the rectangle is less than 30 inches. Write and solve an inequality to find the width of the rectangle.
2(x) + 2(x+3) < 30
2x+2x+6<30
4x+6<30
4x<24
x<6 inches
Ms. Poppleton's Christmas tree topper is what animal
A mouse