Let's go through each question that you mentioned and provide the answers.
Question 6: Which expression is equivalent to 4 - 2(5 - x)?
To solve this, distribute the -2:
\[ 4 - 2(5 - x) = 4 - 10 + 2x = -6 + 2x = 2x - 6 \]
So the correct option is: 2x - 6
Question 12: Find the value of h in the equation -4(5h + 7) + 16h = 40
First, distribute -4:
\[ -20h - 28 + 16h = 40 \]
Combine like terms:
\[ -4h - 28 = 40 \]
Add 28 to both sides:
\[ -4h = 68 \]
Divide by -4:
\[ h = -17 \]
So the correct answer is: h = -17
Question 13: Describe the error and solve correctly for x.
Without the specific equation in question, I can only provide you with a general method. It seems like the options you provided are stating likely errors. In the case of distributing incorrectly, here's what you would check:
If the equation was \( -5(x + 1) = ax + b \), the correct distribution would be \( -5x - 5 \). Check if that was done correctly, and then proceed to solve for \( x \).
Based on the choices, if they did not distribute correctly, then: x = 1; They did not correctly distribute the -5 to both terms in (x + 1) would likely be correct if that matches the context.
Question 14: Find the value of a in the equation 16 - 5a + 2a - 1 = 41 - a
Combine like terms:
\[ 15 - 3a = 41 - a \]
Add \( a \) to both sides:
\[ 15 - 2a = 41 \]
Subtract 15 from both sides:
\[ -2a = 26 \]
Divide by -2:
\[ a = -13 \]
So the correct answer is: a = -13
Question 16: What can you replace the ? with for infinite solutions?
For an equation to have infinite solutions, both sides must be equal in a way that any \( a \) would make the equation true. The expression you provided is \( 2(4 - a) = ? \). The left side is \( 8 - 2a \).
To make both sides equal, you could just substitute \( 8 - 2a \) for ?.
So the correct option is: 4 since both are offset by a factor that doesn’t affect the equality.
Question 18: Find the value of p in the equation -13 + 12p - 4 = 6(2p - 1)
First, simplify:
\[ -17 + 12p = 12p - 6 \]
Subtract \( 12p \) from both sides:
\[ -17 = -6 \]
This is impossible, so there is no solution.
So, the answer is: No Solution
Question 19: Ella is selling a dozen cookies for $4. She had to pay $20 for ingredients. How much will she earn if she sells 12 dozen cookies?
First, calculate the revenue from selling 12 dozen cookies:
Price per dozen = $4, hence for 12 dozen: \[ 12 \times 4 = 48 \]
Now subtract the cost of ingredients: \[ $48 - $20 = $28 \]
So the answer is: $28
If you have any more questions or need further assistance, feel free to ask!
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