Which equation has the same solution for x as this equation: x−12=40 ?(1 point)
Responses
x4=13x over 4 is equal to 13
12−x=40 12 minus x is equal to 40
x+12=−40 x plus 12 is equal to negative 40
x2=14
x−12=40 can be rewritten as x = 52.
The equation that has the same solution for x is: 12−x=40.
he length of a rectangle is four meters less than twice its width.
If the area of the rectangle is 96 m^2, what is the length and the width?
(3 points)
An expression for the length of the rectangle in terms of the width would be ____________
The formula for the area of a rectangle is _____________
Using trial and error, if the area is 96 m^2, then the length and width are ______________
An expression for the length of the rectangle in terms of the width would be:
Length = 2w - 4
The formula for the area of a rectangle is:
Area = length × width
Using trial and error, if the area is 96 m^2, then the length and width are:
Length = 12 meters, Width = 8 meters
Match the equation with its solution(s).(5 points)
3(2i−7)=15
3i+5=3i+7
3i+5=2i−7
3(2i+7)=6i+21
3i+2i−7=18
1. 3(2i−7)=15
Solution: i = 11/6
2. 3i+5=3i+7
No solution. The equation is inconsistent.
3. 3i+5=2i−7
Solution: i = -12
4. 3(2i+7)=6i+21
Solution: i = 0
5. 3i+2i−7=18
No solution. The equation is inconsistent.
A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.
Let n represent the number of notebooks that he buys.
Which inequality describes this scenario?
(1 point)
The inequality that describes this scenario is:
2n + 24 ≤ 37
Solve for b in the following equation: A=1/2(a+b)
To solve for b in the equation A = 1/2(a + b), we can follow these steps:
1. First, multiply both sides of the equation by 2 to eliminate the fraction:
2A = a + b
2. Next, subtract 'a' from both sides of the equation to isolate 'b':
2A - a = b
Therefore, the solution for b is b = 2A - a.
A 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 (3 points)
Identify the property used to arrive at Step 1:
What step includes a mistake made 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.
The mistake made in Step 3 is an error in calculation:
3x = 15 should be corrected to 3x = 13.
The correct answer for x is x = 13.
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 will it take her to only have 30 weeds remaining in the garden?(3 points)
Equation:
Solution:
Meaning of the solution in words:
Equation: 250 - 5x = 30
Solution:
To solve for x, we can subtract 30 from both sides of the equation:
250 - 30 - 5x = 30 - 30
220 - 5x = 0
Then, we can divide both sides of the equation by -5 to isolate x:
(220 - 5x) / -5 = 0 / -5
-44 + x = 0
x = 44
Meaning of the solution in words:
It will take Grandma 44 minutes to only have 30 weeds remaining in the garden at a rate of removing 5 weeds per minute.
he Celsius to Fahrenheit formula: F=9/5C+32
Solve this formula for C. Check all answers that are true.
(4 points)
First step is to multiply by 9 on each side.
First step is to multiply by 9 on each side.
First step is to add 32 to both sides.
First step is to add 32 to both sides.
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
The next step from F - 32 = 9/5 C, could be to divide both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5
Solution: 5/9F - 32 = C
Solution: 5/9F - 32 = C
To solve this equation for C, you would have to distribute at some point.
To solve this equation for C, you would have to distribute at some point.
The correct steps to solve the formula F = (9/5)C + 32 for C are:
1. First step is to subtract 32 from both sides:
F - 32 = (9/5)C
2. The next step is to multiply both sides by 5/9 to isolate C:
(5/9)(F - 32) = C
Hence, the correct solution is: C = (5/9)(F - 32).
The statements about multiplying by 9, adding 32, multiplying by 5, and distributing are incorrect.
Izzie is trying to solve this inequality: 3(t+1)−4t≥−5
After she solves it, she shows it to you and asks you if she did it correctly.
This is the work she completed:
Step 1: 3t+3−4t≥−5
Step 2: −t+3≥−5
Step 3: −t≥−2
Step 4: t≤2
(12 points)
True False
Izzie should not have changed the inequality symbol from ≥ to ≤
True – Izzie should not have changed the inequality symbol from is greater than or equal to to is less than or equal to
False – Izzie should not have changed the inequality symbol from is greater than or equal to to is less than or equal to
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 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 2 to step 3
True – Izzie made a mistake going from step 2 to step 3
False – Izzie made a mistake going from step 2 to step 3
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
The correct answer should have been t≤8
True – The correct answer should have been t is less than or equal to 8
False – The correct answer should have been t is less than or equal to 8
Looking at Izzie's work:
Step 1: 3t+3−4t≥−5
Step 2: −t+3≥−5
Step 3: −t≥−2
Step 4: t≤2
Based on Izzie's work, the following statements are true:
1. Izzie should not have changed the inequality symbol from ≥ to ≤.
False – Izzie correctly changed the inequality symbol from ≥ to ≤ when multiplying by -1 in Step 3.
2. Izzie made a mistake going from step 1 to step 2.
False – Izzie correctly combined like terms in Step 2.
3. Izzie made no mistakes in solving this inequality.
False – Izzie made a mistake in Step 1.
4. Izzie made a mistake going from step 2 to step 3.
False – Izzie correctly subtracted 3 from both sides in Step 2.
5. Izzie made a mistake going from step 3 to step 4.
True – Izzie incorrectly rewrote the inequality symbol from ≥ to ≤.
6. The correct answer should have been t≤8.
False – The correct answer is t≥2, not t≤8.
Therefore, the correct statements are:
- Izzie made a mistake going from step 3 to step 4.
- The correct answer should have been t≥2.
Solve the equation and inequality for x.
Part A: Solve the equation for x showing all steps for credit: ax−5=18
Part B: Solve the inequality for x showing all steps for credit: ax−5>18
Part C: State the difference between an equation and an inequality regarding solving steps and solutions.