l need help with 3 Questions
1) Solve the equation for x. Make sure to show work.
12+3x=6x−4(x−5)
2)For the equation m+3=m+4, can you substitute a value for m to make this a true number sentence? Make sure to explain your answer.
3)The freshman class raised funds for a school dance. It costs $3,000 to rent out the hall plus $15 per student for food and drinks. The freshman class raised $12,000. Write and solve an equation to determine how many students can attend the school dance.
1) To solve the equation 12 + 3x = 6x - 4(x - 5), we can begin by distributing the -4 to the terms inside the parentheses. This gives us 12 + 3x = 6x - 4x + 20. Next, we can combine like terms on the right side of the equation to get 12 + 3x = 2x + 20. To isolate the variable x, we can subtract 2x from both sides of the equation, resulting in 12 + x = 20. Lastly, we subtract 12 from both sides to solve for x, giving us x = 8.
2) In the equation m + 3 = m + 4, we can simplify it by subtracting m from both sides of the equation. This gives us 3 = 4. Since 3 is not equal to 4, no value of m can be substituted to make this a true number sentence.
3) Let's say the number of students attending the dance is represented by s. The equation to determine the number of students can be written as 3000 + 15s = 12000. This equation represents the cost of renting the hall ($3000) added to the cost per student for food and drinks ($15s) equals the total amount raised ($12000) by the freshman class. To solve for s, we can start by subtracting 3000 from both sides of the equation, resulting in 15s = 9000. Finally, we divide both sides by 15 to find that s = 600. Therefore, 600 students can attend the school dance.
Sure! I'd be happy to help you with your questions. Let's tackle them one by one.
1) Solve the equation for x. Make sure to show work.
12 + 3x = 6x - 4(x - 5)
First, simplify the equation by distributing the -4 to (x - 5):
12 + 3x = 6x - 4x + 20
Combine like terms:
12 + 3x = 2x + 20
Next, move the x term to one side of the equation and the constant terms to the other side:
3x - 2x = 20 - 12
Simplify:
x = 8
So, the solution to the equation is x = 8.
2) For the equation m + 3 = m + 4, can you substitute a value for m to make this a true number sentence? Make sure to explain your answer.
In order for the equation m + 3 = m + 4 to be true, the expressions on both sides of the equation must be equal. However, no matter what value we substitute for m, the left side of the equation (m + 3) will always be one less than the right side (m + 4).
Therefore, there is no value of m that can make this equation a true number sentence. The equation is inconsistent.
3) The freshman class raised funds for a school dance. It costs $3,000 to rent out the hall plus $15 per student for food and drinks. The freshman class raised $12,000. Write and solve an equation to determine how many students can attend the school dance.
Let's define a variable to represent the number of students attending the school dance. Let's call this variable "s".
The total cost of the school dance is the cost of renting the hall plus the cost per student for food and drinks. So we can write the equation as:
3000 + 15s = 12000
Now, let's solve for "s".
Subtract 3000 from both sides of the equation:
15s = 12000 - 3000
15s = 9000
Divide both sides of the equation by 15:
s = 9000/15
s = 600
Therefore, 600 students can attend the school dance.
Sure! I can help you with these questions. Let's go through each one step by step.
1) Solve the equation for x:
12 + 3x = 6x - 4(x - 5)
To solve for x, we'll first distribute the -4 to the terms inside the parentheses:
12 + 3x = 6x - 4x + 20
Simplify the equation by combining like terms:
12 + 3x = 2x + 20
Next, we'll isolate the variable x by subtracting 2x from both sides of the equation:
12 + x = 20
Subtract 12 from both sides to get the x-term alone:
x = 20 - 12
Simplify the equation:
x = 8
Therefore, the solution to the equation is x = 8.
2) For the equation m + 3 = m + 4, we need to determine if there exists a value for m that makes the equation a true number sentence.
Let's subtract m from both sides of the equation:
3 = 4
As you can see, no matter what value we substitute for m, the equation will never be true. This means there is no value for m that satisfies the equation. Therefore, the statement m + 3 = m + 4 is always false.
3) To determine how many students can attend the school dance, we'll write and solve an equation based on the given information.
The cost to rent out the hall is $3,000, and each student's food and drinks cost $15. Let's assume the number of students is represented by s.
The total funds raised, $12,000, must cover both the hall rental and the food and drinks costs. So, we can write the equation:
3000 + 15s = 12000
To solve for s, we'll first subtract 3000 from both sides of the equation:
15s = 9000
Next, we'll divide both sides of the equation by 15 to isolate the variable s:
s = 9000 / 15
Simplify the equation:
s = 600
Therefore, the number of students that can attend the school dance is 600.
I hope this helps! Let me know if you have any further questions.