Question

What integer value of n will satisfy both inequalities: n+10>11 and −4n>−12?

A) n=2
B) n=3
C) n=5
D) n=4
E) n=1

Answer 1

The integer value of n that satisfies both n+10>11 and −4n>−12 is n=2. We find that n must be greater than 1 and less than 3 which leaves 2 as the only integer option.

Step-by-step explanation:

The student has asked for the integer value of n that satisfies both inequalities: n+10>11 and −4n>−12.

To solve the first inequality n+10>11, we subtract 10 from both sides:

n + 10 - 10 > 11 - 10
n > 1

This means that n must be greater than 1 to satisfy the first inequality.

Next, for the inequality −4n>−12, we divide both sides by -4, remembering to reverse the inequality sign because we are dividing by a negative number:

-4n / -4 < -12 / -4
n < 3

Now, n must be less than 3 to satisfy the second inequality.

Combining both conditions, n must be an integer that is more than 1 and less than 3. The only integer that fits this condition is n = 2.

Therefore, the correct answer is A) n=2.