The first step to solving almost any problem is to determine what the question is asking and what is given to us to help solve that problem. Looking at the problem statement, they are asking for us to determine which option best describes the value of m in the expression provided. The only thing that we are provided with is an expression which we need to solve for m.
Let's begin to solve the expression for m by first dividing both sides by -5. However, since we are dividing by a negative, that means that we must flip the sign.
Divide both sides by -5
- [tex]-5(m + 1) \le 23[/tex]
- [tex]\frac{-5(m + 1)}{-5} \le \frac{23}{-5}[/tex]
- [tex]m + 1 \ge -\frac{23}{5}[/tex]
The next step that we must take is to subtract 1 from both sides but before that let's convert it into an improper fraction with a denominator of 5 so we can easily deal with it with the other fraction.
Subtract both sides by 1
- [tex]m + \frac{5}{5} - \frac{5}{5} \ge -\frac{23}{5} - \frac{5}{5}[/tex]
- [tex]m \ge -\frac{23}{5} - \frac{5}{5}[/tex]
- [tex]m \ge \frac{-23 - 5}{5}[/tex]
- [tex]m \ge \frac{-28}{5}[/tex]
We have finally came up to our final answer which would state that m is greater than or equal to negative 28 over 5. The options that you have provided seem like the formatting has messed up but I'm sure that on your side you can see the correct answer.
