Question

-0.75<=(n+3)/(-4)<=1 in interval notation. Use decimal form for numerical

Answer 1

To solve the inequality -0.75 ≤ (n+3)/(-4) ≤ 1, we must isolate 'n' by multiplying by -4 and reversing the inequalities. The resulting solution is n between -3.75 and -2, which in interval notation is [-3.75, -2].

Step-by-step explanation:

The inequality -0.75 ≤ (n+3)/(-4) ≤ 1 can be solved by considering the two-sided inequality separately. We'll solve for 'n' by multiplying all parts of the inequality by -4, which will reverse the inequalities due to the multiplication of a negative number, and then isolating 'n'. Remember to respect the direction of the inequalities while performing the operations.

First, multiplying everything by -4:

• 3 ≥ -4*(n+3) ≥ -4

Next, distribute the -4:

• 3 ≥ -4n - 12 ≥ -4

Then, add 12 to all parts of the inequality:

• 15 ≥ -4n ≥ 8

Finally, divide by -4, remembering to reverse the inequalities:

• -3.75 ≤ n ≤ -2

In interval notation, this is written as [-3.75, -2].