Answer:
-19, -18, -17
Step-by-step explanation:
1. To find the sum of three consecutive integers, we can use the formula [tex]x + x + 1 + x + 2[/tex], where x = first term. As you can see from the formula, + 1 is the next term, and + 2 is the following term after that.
2. (Solving)
Step 1: Combine like terms.
- [tex](x + x + x) + (1+2) = -54[/tex]
- [tex]3x + 3 = -54[/tex]
Step 2: Subtract 3 from both sides.
- [tex]3x + 3 - 3 = -54 - 3[/tex]
- [tex]3x = -57[/tex]
Step 3: Divide both sides by 3.
- [tex]\frac{3x}{3} = \frac{-57}{3}[/tex]
- [tex]x = -19[/tex]
3. Now that we know our first term is -19, let's apply it to [tex]x + x + 1 + x + 2[/tex].
- [tex](-19) + (-19+1) + (-19+2)[/tex]
- [tex]-19 + (-18) + (-17)[/tex]
4. Okay, so we got that the integers are -19, -18, and -17. Let's check if these numbers sum to -54.
Therefore, the integers are -19, -18, and -17.
