Me on this question ! an inequality is shown below: −np − 6 ≤ 3(c − 5) which of the following solves for n?

Me on this question ! an inequality is shown below: −np − 6 ≤ 3(c − 5) which of the following solves for n? n ≥ − the quantity 3 times c minus 21 all over p n ≥ − the quantity 3 times c minus 9 all over p n ≤ − the quantity 3 times c minus 21 all over p n ≤ − the quantity 3 times c minus 9 all over p

Answers

It is the 2 sentence

The correct option is B) ngeq frac{-3c+9}{p}.

Step-by-step explanation:

Consider the provided inequality:

-np - 6 leq 3(c - 5)

Now distribute 3 inside the parentheses.

-np - 6leq 3c - 15

Add 6 on both the side of the inequality:

-np-6+6leq 3c-15+6

-npleq 3c-9

Now, multiply both the sides by a negative sign and reverse the sign of inequality.

npgeq -3c+9

Divide both the sides of the inequality by p.

ngeq frac{-3c+9}{p}

Now consider the provided options.

By observing the provided option it can be concluded that the correct option is B) ngeq frac{-3c+9}{p}.

-np - 6 < = 3(c-5)
-np - 6 < = 3c - 15
-np < = 3c - 15 + 6
-np < = 3c - 9
n > =  (-3c + 9)/p

 Rightarrow ngeqfrac{9-3c}{p}

Step-by-step explanation:

We have been given the inequality

−np − 6 ≤ 3(c − 5)

We will solve for n

So, firstly we will shift 6 on right hand side of the inequality we get:

-npleq3(c-5)+6

Now, we will open the parenthesis on right hand side of the inequality;

-npleq3c-15+6

-npleq3c-9

-nleqfrac{3c-9}{p}

Rightarrow ngeqfrac{9-3c}{p}

n ≥ − the quantity 3 times c minus 9 all over p

Step-by-step explanation:

To solve inequalities you should use the same method as to solve equalities.

1. First write down the inequality:

-np-6leq 3(c-5)

2. Solve the parentheses:

-np-6leq 3c-15

3. Pass the independent numbers to the right side of the inequality with opposite sign and do the mathematical operations:

-npleq 3c-15+6\\-npleq 3c-9

4. Pass the p with the minus sign to the right side of the inequality, as p has the minus sign, the direction of the inequality changes:

ngeq -(frac{3c-9}{p})

B
c>=3 and n<0 and p<=(9-3 c)/n

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