Solve the inequality. Graph and check your solutions.

Question

1/4>n+4

Answer 1

To solve the inequality 1/4 > n + 4, we can start by isolating the variable n.

1/4 > n + 4

We can start by subtracting 4 from both sides:

1/4 - 4 > n + 4 - 4

-15/4 > n

Next, we can simplify the inequality by finding a common denominator:

-15/4 = -3.75

So, the simplified inequality is:

-3.75 > n

To graph this inequality, we will graph the line n = -3.75 as a dashed line (since the inequality does not include "equal to"). Then, since we want n to be less than -3.75, we shade the region to the left of the line.

Checking the solutions, we can test a value, such as n = -4, to see if it satisfies the inequality:

1/4 > -4 + 4

1/4 > 0

Since 1/4 is indeed greater than 0, n = -4 is a valid solution.

Therefore, the solution to the inequality is n < -3.75.