Question

The sum of three consecutive integers is -54. What are the integers?

Answer 1

Answer:

-19, -18, -17

Step-by-step explanation:

1. To find the sum of three consecutive integers, we can use the formula $x + x + 1 + x + 2$, 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.

• $(x + x + x) + (1+2) = -54$
• $3x + 3 = -54$

Step 2: Subtract 3 from both sides.

• $3x + 3 - 3 = -54 - 3$
• $3x = -57$

Step 3: Divide both sides by 3.

• $\frac{3x}{3} = \frac{-57}{3}$
• $x = -19$

3. Now that we know our first term is -19, let's apply it to $x + x + 1 + x + 2$.

• $(-19) + (-19+1) + (-19+2)$
• $-19 + (-18) + (-17)$

4. Okay, so we got that the integers are -19, -18, and -17. Let's check if these numbers sum to -54.

• $-19 - 18 - 17$

• $-37 -17$

• $-54$

Therefore, the integers are -19, -18, and -17.