Sure, let's solve the inequality [tex]\(-2m - 1 > m\)[/tex] step by step.
### Step 1: Simplify the Inequality
First, move all terms involving [tex]\(m\)[/tex] to one side to combine like terms.
[tex]\[ -2m - 1 > m \][/tex]
Subtract [tex]\(m\)[/tex] from both sides:
[tex]\[ -2m - 1 - m > 0 \][/tex]
### Step 2: Combine Like Terms
Combine the [tex]\(m\)[/tex] terms on the left-hand side:
[tex]\[ -3m - 1 > 0 \][/tex]
### Step 3: Solve for [tex]\(m\)[/tex]
Now we need to isolate [tex]\(m\)[/tex]. Add 1 to both sides to move the constant term to the right-hand side:
[tex]\[ -3m > 1 \][/tex]
Next, divide both sides by [tex]\(-3\)[/tex]. Remember that when you divide an inequality by a negative number, you need to reverse the inequality sign:
[tex]\[ m < -\frac{1}{3} \][/tex]
### Step 4: Determine the Solution Interval
The inequality [tex]\(m < -\frac{1}{3}\)[/tex] indicates that [tex]\(m\)[/tex] can be any number less than [tex]\(-\frac{1}{3}\)[/tex].
### Final Answer
The set of solutions can be written in interval notation as:
[tex]\[ m \in (-\infty, -\frac{1}{3}) \][/tex]
So, the solution to the inequality [tex]\(-2m - 1 > m\)[/tex] is [tex]\( m < -\frac{1}{3} \)[/tex].
