Question

An inequality is shown: −np − 4 ≤ 2(c − 3). Which of the following solves for n?

a) n ≤ the quantity 2 times c minus 2 all over negative p
b) n ≤ the quantity 2 times c minus 10 all over negative p
c) n ≥ the quantity 2 times c minus 2 all over negative p
d) n ≥ the quantity 2 times c minus 10 all over negative p

Answer 1

To solve the inequality −np − 4 ≤ 2(c − 3) for n, we add 4 to both sides, simplify, and then divide by −p, which reverses the inequality, giving us the solution n ≥ (2c − 2)/−p.

Step-by-step explanation:

The student is asking about solving an inequality for a specific variable (n). The inequality given is −np − 4 ≤ 2(c − 3). To solve for n, we'll manipulate the inequality step by step:

• Add 4 to both sides: −np ≤ 2c − 6 + 4
• Simplify the right side: −np ≤ 2c − 2
• Divide by −p (and remember that dividing by a negative number reverses the inequality): n ≥ ²/±c − 2/±p

Therefore, the correct answer is (c) n ≥ the quantity 2 times c minus 2 all over negative p.