To solve the inequality, we will first simplify it step by step.
Starting with:
18 – 3n < 2n + 20 - 4n
First, let’s combine like terms on the right side:
18 – 3n < (2n - 4n) + 20
This simplifies to:
18 – 3n < -2n + 20
Next, we want to isolate the variable. Let’s add 3n to both sides:
18 < -2n + 3n + 20
This simplifies to:
18 < n + 20
Now, we will subtract 20 from both sides:
18 – 20 < n
This results in:
-2 < n
We can rewrite this as:
n > -2
Thus, the solution set is all real numbers greater than -2. In interval notation, this is expressed as:
(-2, ∞)
In conclusion, the solution set for the inequality 18 – 3n < 2n + 20 - 4n is n > -2.