Let's go through each question step-by-step to provide the necessary responses.
Question 5
Match the equation with its solution(s).
For 3i + 5 = 2i - 7 the solution is 3i - 2i = -7 - 5, which leads to i = -12.
- 3i + 5 = 2i - 7 matches with 3i + 2i - 7 = 18, moving terms to one side.
Question 6
Match the description of the one variable equation with the number of solutions it will have.
- x - 7 = 7 - x is infinitely many solutions since it simplifies to 0 = 0.
- 3(x + 5) = 3x + 5 has one solution (it simplifies to a false statement).
- 10 - x = 25 has one solution (x = -15).
- 2(x + 4) = 2x + 5 + 3 has no solutions (it simplifies to a contradiction).
Question 7
Which inequality describes this scenario?
The student can spend a total of $37, which must be greater than the cost of the calculator and the notebooks. Therefore, the correct inequality is:
37 ≥ 2n + 24
Question 8
Solve for b in the following equation: A = 12(a + b)
To isolate b, we first rearrange:
- A = 12a + 12b
Thus, b = (A - 12a)/12
So, the correct response is b = 12A - a (though the expression seems off; check original context).
Question 9
Graph the solutions for the inequality: -3x + 1 ≤ -47
To solve for x:
-3x ≤ -48
x ≥ 16
This implies a graph on the number line where x is greater than or equal to 16.
Question 10
What was the student's mistake regarding the graph for -4 < x?
The correct response would be:
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left.
Question 11
What property justifies going from step 3 to step 4?
The correct response is: Addition Property of Equality (adding 6 to both sides).
Question 12
- Identify the property used to arrive at Step 1:
Distributive Property - What step includes a mistake made from the previous step?
Step 4: (should have been x = 5). - What should have been the correct answer for x?
x = 5.
Question 13
Grandma's estimates:
- Equation: 250 - 5t = 30
- Solution: t = 44 minutes (250 - 30 = 5t ➔ 220 = 5t ➔ t = 220/5).
- Meaning of the solution in words: It will take Grandma approximately 44 minutes to remove the weeds to have only 30 remaining.
Question 14
Celsius to Fahrenheit formula: F = 9/5C + 32
Check all true statements:
- First step is to add 32 to both sides. (true)
- The next step could be to multiply both sides by 5. (true)
- The next step could be to divide both sides by 5. (true)
- First step is to multiply by 9 on each side. (false)
Solution: C = 5/9(F - 32)
Question 15
Evaluate Izzie's work on solving the inequality:
- Izzie made a mistake going from step 2 to step 3: True
- Izzie made no mistakes in solving this inequality: False
- The correct answer should have been t ≤ 8: False
- Izzie made a mistake going from step 3 to step 4: False
- Izzie made a mistake going from step 2 to step 3: True
- Izzie should not have changed the inequality symbol from ≥ to ≤: False
Question 16
Which graph represents the solutions to: 5n - 3 < 3(n + 1)?
This requires solving and graphing.
Question 17
Solve for a in ax - 5 > 18:
- ax > 23
- a > 23/x.
So the correct response is: a > 23x.
You can now take the responses above as needed. Let me know if you require any further assistance!