Steps of Solving
What is the the first step called for solving this equation?
- (3x - 8)+6x=56
Distributive Property
Solve:
x/5 - 7 = 4
x = 55
Solve 3(2x - 5) = 5(x - 3)
x=0
If x represents the first integer, this algebraic expression represents the sum of three consecutive integers.
x + x + 1 + x + 2
A school purchases 3 adult tickets and 5 student tickets for a field trip. An adult ticket costs $4 more than a student ticket. The school pays a total of $84. Fill in the table.
Cost Number of Tickets Total
_________________________________________
Student s
________________________________________
Adult
________________________________________
Total $84
Cost Number of Tickets Total
Student s 5 5s
Adult s + 4 3 3(s + 4)
Total 8 $84
What's the first step of the equation and do it.
(2(m-4))/3+2 = -18
Subtract 2 on both sides
Distribute 2 to the m and -4
Multiply all terms by 3
Solve -4x + 12 = -20
x = 8
Solve: 2(2x + 3) + 5x - 4 = 29
x = 3
If x represents the first odd integer, these algebraic expressions represent the next two consecutive odd integers.
x + x + 2 + x + 4
Ava buys 3 boxes of popcorn and 2 candy bars. The popcorn costs $3 more per box than the candy bars. She pays a total of $29. What is the cost of 1 box of popcorn?
Cost Amount Total
_________________________________________
Popcorn p
________________________________________
Candy bars
________________________________________
Total $
x = $6
Solve:
(3(x+3))/3 = 6
x=3
Solve -(3x + 5) -3x = -8
x = 1/2
Solve:
5x-2(x+3)=2(x-3)+9
x=6
The three consecutive integers whose sum is 210.
69, 70, 71
A scientist mixes a 20% acid solution with a 50% acid solution to make 12 liters of a 30% acid solution. How many liters of each solution should be used? (HINT: DRAW BUCKETS)
4L of 50% and 10L of 20%
4(x−3)+2=18
Step 1: 4x−12+2=18 __________
Step 2: 4x−10=18 __________
Step 3: 4x−10+10=18+10 __________
Step 4: 4x=28 __________
Step 5: x=7 __________
1. Distributive Property
2. Combine Like Terms
3. Addition Property of Equality
4. Combine Like Terms
5. Division Property of Equality
-3(x + 2) - 2(x - 5) = -31
x = 7
Solve:
(2(x - 5))/3 - 3 = 1
x = 11
The three consecutive odd integers whose sum is 153.
49, 51, 53
Liam buys 5 pounds of apples and 2 pounds of oranges. Oranges cost $1 more per pound than apples. He pays a total of $19. What is the combined cost of 1 pound of apples and 1 pound of oranges?
$4
Order the reasons for the steps using the word bank.
6(x+1)=4(x+4)
Step 1: 6x+6=4x+16 __________________
Step 2: 6x−4x+6=16 __________________
Step 3: 6x−4x=10 __________________
Step 4: 2x=10 __________________
Step 5: x=5 __________________
1. Distributive Property
2. Subtraction Property of Equality
3. Subtraction Property of Equality
4. Combine Like Terms
5.Division Property of Equality
Solve:
(3(x-8))/2 = -18
x = -4
Solve:
4x+1/2(6x+8)-2=23
x = 3
If the sum of three consecutive even integers is 162, this is the value of the largest integer.
56
Noah buys 2 T-shirts and 4 hats. Each T-shirt costs $8 more than a hat. He spends a total of $64. What is the combined cost of 1 T-shirt and 1 hat?
$18