Question
A student solves the following problem:
Problem:
2(x−3) + 3x = 19
Step 1: 2x − 6 + 3x = 19 Click and drag to move
Step2: (2x + 3x) −6 = 19 Click and drag to move
Step 3: 5x − 6 = 19 Click and drag to move
Step 4: 5x −6 + 6 = 19 + 6 Click and drag to move
Step 5: 5x = 25 Click and drag to move
Step 6: x = 5 Click and drag to move
What property justifies going from step 3 to step 4?
The property that justifies going from step 3 to step 4 is the addition property of equality. This property states that if you add the same number to both sides of an equation, the equality is maintained. In this case, 6 is added to both sides of the equation.
student solved the equation: x+2(x+1)=17
Step 1: x+2x+2=17
Step 2: 3x+2=17
Step 3: 3x=15
Step 4: x=45
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Identify the property used to arrive at Step 1:
What Step includes a mistake from the previous step?
What should have been the correct answer for x?
The property used to arrive at Step 1 is the distributive property.
Step 2 includes a mistake from the previous step. The correct calculation for Step 2 should be: 3x + 2 = 17.
The correct answer for x should have been x = 5.
Grandma is removing weeds from her garden. She estimates that there are 250 weeds in the garden at the moment, and she can remove weeds at a rate of 5 per minute. At this rate how many minutes (m) will it take her to only have 30 weeds remaining in the garden?
To find the number of minutes it will take Grandma to have 30 weeds remaining in the garden, we need to determine the number of times she needs to remove 5 weeds until there are only 30 left.
First, we need to find the difference between the initial number of weeds and the desired number of weeds: 250 - 30 = 220.
Next, we divide this difference by the rate at which Grandma can remove the weeds: 220 / 5 = 44.
Therefore, it will take Grandma 44 minutes to only have 30 weeds remaining in the garden.
Grandma is removing weeds from her garden. She estimates that there are 250 weeds in the garden at the moment, and she can remove weeds at a rate of 5 per minute. At this rate how many minutes (m) will it take her to only have 30 weeds remaining in the garden?(3 points)
Equation:
250 - 5m = 30
Solution:
m = 44
Meaning of the solution in words:
The solution m = 44 means that it will take Grandma 44 minutes to remove enough weeds from her garden to have only 30 remaining.
The Celsius to Fahrenheit formula: F=95C+32
Solve this formula for C. Check all answers that are true.
(2 points)
Responses
First step is to multiply by 9 on each side.
First step is to multiply by 9 on each side.
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
Solution: 5/9F - 32 = C
Solution: 5/9F - 32 = C
First step is to add 32 to both sides.
To solve this equation for C, you would have to distribute at some point.
To solve the formula F = 95C + 32 for C, you need to perform the following steps:
Step 1: Subtract 32 from both sides to isolate the 95C:
F - 32 = 95C
Step 2: Divide both sides by 95 to solve for C:
C = (F - 32) / 95
The correct solutions are:
Solution: C = (F - 32) / 9
Solution: C = (5/9)(F - 32)
You do not need to distribute in this equation.
Izzie is trying to solve this inequality: 3(t+1)−4t≥−5
After she solves it, she shows it to you, and she asks you if she did it correctly.
This is the work she completed:
3t+3−4t≥−5
−t+3≥−5
−t≥−8
t≥8
(2 points)
True False
Izzie made no mistakes in solving this inequality
True – Izzie made no mistakes in solving this inequality
False – Izzie made no mistakes in solving this inequality
Izzie made a mistake going from step 3 to step 4
True – Izzie made a mistake going from step 3 to step 4
False – Izzie made a mistake going from step 3 to step 4
Izzie made a mistake going from step 1 to step 2
True – Izzie made a mistake going from step 1 to step 2
False – Izzie made a mistake going from step 1 to step 2
Izzie forgot to change the inequality symbol to be t≤8
True – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
False – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
Izzie should have had the answer t≤−8