Sure! I will answer each question in the order given.
Question 2
To determine which equation has a different value of \( x \):
A. \( x - 0.025 = 0.6 \)
- \( x = 0.6 + 0.025 = 0.625 \)
B. \( x - \frac{7}{8} = -\frac{3}{2} \)
- \( x = -\frac{3}{2} + \frac{7}{8} \)
- \( x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \)
C. \( x + 0.875 = 1.5 \)
- \( x = 1.5 - 0.875 = 0.625 \)
D. \( x + \frac{9}{8} = \frac{7}{4} \)
- \( x = \frac{7}{4} - \frac{9}{8} \)
- \( x = \frac{14}{8} - \frac{9}{8} = \frac{5}{8} \)
The values of \( x \) are:
- A: 0.625
- B: -0.625
- C: 0.625
- D: 0.625
Answer: B. \( x \) has a different value \( (-0.625) \) compared to the others (0.625).
Question 3
To find the equation that represents the number of boxes Trina sold:
Total boxes sold = 37, and Yuri sold 14 boxes:
- \( n + 14 = 37 \)
Solving for \( n \):
- \( n = 37 - 14 = 23 \)
Answer: A. \( n + 14 = 37; \) Trina sold 23 boxes.
Question 4
The cost of a pizza slice is $3.19, and the cost of a drink is \( x \). The total cost is $5.61:
The equation can be set up as: \( x + 3.19 = 5.61 \)
Solving for \( x \): \( x = 5.61 - 3.19 = 2.42 \)
Answer:
- \( x + 3.19 = 5.61 \)
- \( x = 2.42 \)
Question 5
Given \( \frac{x}{-5} = 2 \): Multiplying both sides by -5: \( x = 2 \times -5 = -10 \)
Answer: \( x = -10 \)
Question 6
To check which equations have the same solution:
A. \( -\frac{3}{4}x = \frac{5}{2} \) and \( \frac{5}{2}x = -\frac{3}{4} \) ⇒ Different forms, need to be compared.
B. \( \frac{3}{8}x = 1 \) ⇒ \( x = \frac{1}{3} \times 8 = \frac{8}{3} \) \( \frac{1}{3}x = \frac{1}{8} \) ⇒ \( x = \frac{1}{8} \times 3 = \frac{3}{8} \) Same solution!
C. \( \frac{x}{3.2} = 1.8 \) and \( 1.8x = 3.2 \) ⇒ Different forms, will need to be simplified.
D. \( -3.2x = 0.64 \) and \( \frac{x}{4} = -0.05 \) ⇒ Different solutions.
After solving or analyzing: Answer: C. \( x/3.2=1.8 \) and \( 1.8x=3.2 \) => Same solution.
Question 7
The equation \( 3x = 24 \) can represent:
Answer: B. Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?
Question 8
For the temperature that dropped by 12 degrees in 5 hours:
The equation can be set up as: \( 5x = 12 \)
Solving for \( x \): \( x = \frac{12}{5} = 2.4 \) degrees per hour.
Answer:
- \( 5x = 12 \)
- The temperature decreased by \( 2.4 \) degrees every hour.
Question 9
If we analyze the tiles, the expression is: \( x - 1 - 1 - 1 - 1 - 1 - 1 = 0 \) which implies: \( x - 6 = 0 \) ⇒ \( x = 6 \)
The answer options indicate: General simplification or the solution implies:
Answer: Requires correct verification from algebra tiles; solution would depend on specific form.
Question 10
To find the equation with the solution of \( -7 \):
A. \( -3(-7) - 8 = -29 \) ⇒ True B. \( -(-7) + 3 = -4 \) ⇒ False C. \( 5(-7) + 11 = -24 \) ⇒ True D. \( 4(-7) - 23 = 5 \) ⇒ False
Answer: A. \( -3x - 8 = -29 \)
Question 11
To find the equation with a solution differing from the others:
A and B require solving. If solved correctly, we can differentiate which outputs deviate.
Answer: Details require formatting of given output to check; pending terms where practicality arises.
Question 12
For the guitar practice: Let \( x \) = number of weekdays, \( p = 30 \) min daily:
\( 30x + 50 = 140 \)
Answer: \( 30x + 50 = 140 \)
Please let me know if further details or corrections are required!
9 answers