Question

1. the sum of three consecutive integers is 33. what are the three integers? show all work for full credit.

Explanation:

Step1: Define the integers

Let the first integer be $x$. The next two consecutive integers are $x+1$ and $x+2$.

Step2: Set up the sum equation

The sum equals 33, so:
$$x + (x+1) + (x+2) = 33$$

Step3: Simplify the left side

Combine like terms:
$$3x + 3 = 33$$

Step4: Isolate the variable term

Subtract 3 from both sides:
$$3x = 33 - 3$$
$$3x = 30$$

Step5: Solve for $x$

Divide both sides by 3:
$$x = \frac{30}{3} = 10$$

Step6: Find the other integers

Calculate $x+1 = 10+1=11$, $x+2=10+2=12$

Answer:

The three consecutive integers are 10, 11, and 12.