### Instruction: Solve the inequality
\[2 - \frac{1}{2x + 3} < 4.\].### Response: To solve this inequality, I want to isolate x and find out which values make the inequality true.
First, I notice that there is a fraction on the left side, and I want to get rid of it by multiplying both sides by the denominator.
However, before I do that, I need to check if the denominator could be zero, because that would make the fraction undefined and the inequality meaningless.
The denominator is zero when x = -3/2, so I will exclude that value from the solution set.
Now, I multiply both sides by 2x + 3 and get
\[2(2x + 3) - 1 < 4(2x + 3).\]
I simplify this by expanding and combining like terms, and I get
\[4x + 5 < 8x + 12.\]
Next, I want to bring all the x terms to one side and the constants to the other, by subtracting 4x from both sides and subtracting 12 from both sides.
This gives me
\[-7 < 4x.\]
To isolate x, I divide both sides by 4, and I get
\[-\frac{7}{4} < x.\]
This means that x can be any number that is greater than -7/4, except for -3/2, which makes the fraction undefined.
Therefore, the solution set is the interval (-7/4, -3/2) union (-3/2, infinity), using interval notation.