Sure, let's solve the equation step-by-step to determine what Nathaniel will actually evaluate.
The given equation is:
[tex]\[ -3m = 4m - 15 \][/tex]
First, we want to combine like terms by bringing all the terms involving [tex]\(m\)[/tex] to one side. To do this, add [tex]\(3m\)[/tex] to both sides of the equation:
[tex]\[ -3m + 3m = 4m - 15 + 3m \][/tex]
This simplifies to:
[tex]\[ 0 = 7m - 15 \][/tex]
Next, we need to isolate [tex]\(m\)[/tex]. To do this, add 15 to both sides of the equation:
[tex]\[ 0 + 15 = 7m - 15 + 15 \][/tex]
Simplifying, we get:
[tex]\[ 15 = 7m \][/tex]
To solve for [tex]\(m\)[/tex], divide both sides by 7:
[tex]\[ m = \frac{15}{7} \][/tex]
Now, let's look at the given options to see which expression Nathaniel will evaluate to get this result:
1. [tex]\( 4 + 15 - 3 \)[/tex]
2. [tex]\( 4 - 15 + 3 \)[/tex]
3. [tex]\( \frac{-15}{-3-4} \)[/tex]
4. [tex]\( -15 - \frac{-3}{4} \)[/tex]
To find the correct expression, let's evaluate the third option:
[tex]\[ \frac{-15}{-3-4} = \frac{-15}{-7} \][/tex]
The negative signs cancel out, giving:
[tex]\[ \frac{15}{7} \][/tex]
Therefore, the expression [tex]\( \frac{-15}{-3-4} \)[/tex] is indeed what Nathaniel will evaluate when solving the equation. The equivalent option in our list is:
[tex]\[ \frac{-15}{-3-4} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{\frac{-15}{-3-4}} \][/tex]
