Solve Equations with Variables on Both Sides
-2a - 9 = 6a + 15
a=-3
7+y=5(2y-1)+3y
y=1
Tyrone has already typed 100 words for an essay and can type 35 words per minute. Vanessa has already typed 120 words and can type 30 words per munite. In how many minutes will Tyrone and Vanessa have typed the same number of words?
100+35m = 120+30m; 4 minutes
7(m+2)-5=1/3(21m+9)-6
no solution
-8 ≤ -6x +10
x ≤ 3
closed circle at 3, shading to the left
10 - 3x = -5 + 2x
x=3
6x-3(x-1)=2(x+8)-6
x = 7
Leo's Lawn Mowing Service has $300 in start-up expenses, and charges $30 for each yard. Yan's Yards does not have any start-up expenses and charges $20 for each yard. After how many yards will the profits of the two businesses be the same?
30x-300=20x; 30 yards
-3x + -3(4-3h)=-12(1-h)-3h
-1.7x+4.9 < -8.7
x > 8
open circle at 8, shading to the right
4.06x + 3.22 = 27.16 - 1.26x
x = 4.5
3.1-(x+4.7) = 5.2(x-2)-3.6
x = 2
A baseball player averages 2 hits per game. The player alread has 18 hits this season. Another player has 22 hits so far this season and averages 1 hit per game. After how many games will both players have the same number of hits?
18+2g = 22+g; 4 games
no solution
-2/7x + 1/2 ≤ 4/7
x ≥ -1/4
closed circle at -1/4 and shading to the right
1/2x - 5 = 10 - 3/4x
x = 12
0.1(y+2) = 4(0.2y-0.3)
x = 2
The school rectangular cafeteria has a perimeter of 401 feet. The length of the cafeteria is 5 feet less than 0.75 times the width. What is the width of the cafeteria?
401=2(0.75w-5)+2w; w=117.43 feet
Complete so the equation has infinitely many solutions
15f+24-6t-8-2t=___t - _____
7t-16
Juanita has $25, and she makes $11 per hour. She needs at least $58 to buy new shoes. Write and solve an inequality to determine how many hours Juanita must work to be able to buy new shoes. Then interpret the solution.
11x + 25 ≥ 58; x ≥ 3; Juanita must work at least 3 hours to buy new shoes
7-16y + 6 = 8 + 3/8y
y=16
-9+1/4(8n+16) = 1/4(20n+4)
The cafeteria offeres two snack options as shown in the table. Out of 18 students; 8 students choose Option B and the rest choose Option A. If the total cost of option A is the same as option B, what is the price of a carton of milk?
Option A: Option B:
Milk: $x each Juice Box: $2x each
Bag of Peanuts: $1 Apple: $0.50
8(2x+0.50) = 10(x+1); $1.00
5(-3h-4)-2h= _____h - _____
-17h - (any number but 20)
Emmett has $52 in his wallet. He rents a bicycle to travel around the city for $4.50 per hour. Emmett wants to have at least $25 left after the bicycle rental. Write and solve an inequality to determine how long Emmett can rent the bicycle. Then interpret the solution.
52 - 4.50x ≥ 25; x ≤ 6; Emmett can rent the bicycle for at most 6 hours