An inequality is shown below:
−np − 3 ≥ 7(c − 4)
Which of the following solves for n?
n ≤ − the quantity 7 times c minus 31 all over p
n ≤ − the quantity 7 times c minus 25 all over p---my choice
n ≥ − the quantity 7 times c minus 31 all over p
n ≥ − the quantity 7 times c minus 25 all over p
I agree if you got
-(7c - 25)/p
Well, solving inequalities can be a bit tricky, but don't worry, I'm here to make it fun for you!
Let's crack this inequality like a piñata at a birthday party! Buena suerte!
To solve for n in the given inequality −np − 3 ≥ 7(c − 4), we'll go through the options one by one.
So, let's start with your choice: n ≤ − the quantity 7 times c minus 25 all over p.
Hmm, let's see if this choice knocks it out of the park like a clown at a circus!
When we substitute n as - the quantity 7 times c minus 25 all over p in the original inequality, we get:
−(- the quantity 7 times c minus 25 all over p)p − 3 ≥ 7(c − 4)
Simplifying that expression, we get:
(7c - 25) - 3 ≥ 7(c - 4)
Now, let's take it step by step, shimmying and shuffling like a funky clown!
First, we'll distribute 7 on the right side:
7c - 25 - 3 ≥ 7c - 28
Then, combine like terms:
7c - 28 ≥ 7c - 28
Woah, look at that! The variables cancel out, leaving us with a true statement!
So, what's the conclusion, my friend?
In this case, any value of n will satisfy the inequality! It means that n can be any number, like a clown with unlimited tricks up its sleeve!
Therefore, none of the given options solve for n. Keep hunting for the correct one, just like hunting for the perfect punchline!
To solve for n in the given inequality −np − 3 ≥ 7(c − 4), we need to isolate n on one side of the inequality.
Step 1: Distribute the 7 on the right side of the inequality:
−np − 3 ≥ 7c − 28
Step 2: Move the constant term to the other side of the inequality by adding 3 to both sides:
−np ≥ 7c − 28 + 3
−np ≥ 7c − 25
Step 3: Divide both sides of the inequality by -p. Remember, when dividing an inequality by a negative number, the inequality sign changes direction:
n ≤ (7c − 25) / p
Therefore, the correct solution for n is n ≤ − the quantity 7 times c minus 25 all over p.
To solve the inequality −np − 3 ≥ 7(c − 4) for n, we need to isolate n on one side of the inequality sign. Let's go through the steps together:
Step 1: Distribute the 7 on the right side of the inequality:
−np − 3 ≥ 7c − 28
Step 2: Combine like terms by bringing all terms containing n to one side of the inequality:
−np ≥ 7c − 28 + 3
Step 3: Simplify the right side of the inequality:
−np ≥ 7c − 25
Step 4: Divide both sides of the inequality by -p (note: if p is positive, the inequality sign will remain the same, but if p is negative, the inequality sign will flip):
n ≤ (7c − 25) / p
So, the solution for n is n ≤ (7c − 25) / p. This matches your choice: n ≤ − the quantity 7 times c minus 25 all over p. Well done!