Question

Two consecutive integers have the following property. When the smaller integer is added to three times the larger integer, the result is two less than five times the smaller integer. Which equation can be used to find the integers and what is the value of x?

Option 1: Equation: X+3X+1= 5X-2 Solution: x=3
Option 2: Equation: X+3(X+1) = 5X-2 Solution: x=5
Option 3: Equation: X+3(X+1) = 2-5x Solution: x=-1/9
Option 4: Equation: X+3X+1=2-5X Solution: x=1/9

Answer 1

The correct equation to find the two consecutive integers is X + 3(X + 1) = 5X - 2 (Option 2), and after solving, the correct value of X is 5, which means the integers are 5 and 6.

Step-by-step explanation:

The equation to find two consecutive integers where the smaller integer added to three times the larger results in two less than five times the smaller integer is represented by Option 2:

X + 3(X + 1) = 5X - 2.

Let's solve the equation step by step:

1. X + 3(X + 1) means X + 3X + 3.
2. Combine like terms: 4X + 3.
3. Set the equation equal to 5X - 2: 4X + 3 = 5X - 2.
4. Subtract 4X from both sides to get X on one side: 3 = X - 2.
5. Add 2 to both sides so X equals 5.

The correct value of X is 5, and the consecutive integers are 5 and 6.