Solve the inequality. Graph and check your solutions.
3/2 < n+2
n
To solve the inequality, we need to isolate the variable n.
Starting with the given inequality:
3/2 < n + 2
Subtracting 2 from both sides:
3/2 - 2 < n
Converting 2 to 4/2 for better compatibility with the left side:
3/2 - 4/2 < n
Combining the fractions:
-1/2 < n
So, the inequality is -1/2 < n.
To graph this inequality on a number line, we plot an open circle at -1/2, since it is not included in the solution set. Then, we shade to the right of the open circle to represent all the values of n that are greater than -1/2.
Checking the solution, let's pick a number greater than -1/2, such as 0.
Plugging n = 0 into the original inequality:
3/2 < 0 + 2
3/2 < 2, which is true.
Therefore, n = 0 is a valid solution.
Hence, the solution to the inequality is -1/2 < n, and the graph confirms this.