Question

solve the inequality. graph the solution set, and write the solution set in set - builder notation and interval notation. write the numbers as simplified fractions or integers. \\(3(m + 2)+m>4(m + 4)+17\\) part: 0 / 3 part 1 of 3 the solution set in set - builder notation is

Explanation:

Step1: Expand both sides

First, we expand the expressions on both sides of the inequality \(3(m + 2)+m>4(m + 4)+17\).
Using the distributive property \(a(b + c)=ab+ac\), we get:
\(3m+6 + m>4m+16 + 17\)

Step2: Combine like terms

Combine the like terms on each side.
On the left - hand side: \(3m+m = 4m\), so the left - hand side becomes \(4m + 6\).
On the right - hand side: \(16+17=33\), so the right - hand side becomes \(4m+33\).
The inequality now is \(4m + 6>4m+33\).

Step3: Subtract \(4m\) from both sides

Subtract \(4m\) from both sides of the inequality:
\(4m+6-4m>4m + 33-4m\)
Simplifying both sides, we have \(6>33\).

Since \(6>33\) is a false statement, this means that there are no real numbers \(m\) that satisfy the inequality.

Answer:

The solution set in set - builder notation is \(\{m\in\mathbb{R}\mid\text{no solution}\}\) (or we can also write it as \(\varnothing\) (the empty set)). In interval notation, the solution set is \(\varnothing\) (the empty interval).