Question

The sum of three consecutive integers is equal to twice the 2nd number decreased by 14. Write an equation and determine the 3 consecutive integers

Answer 1

Let lowest integer be x then the second and third are x+1 and x+2.

x + x + 1 + x + 2 = 2(x + 1) - 14

3x + 3 = 2x - 12

x = -12 - 3 = -15

answer is -15, -14 and -13

Answer 2

Givens

Let the smallest integer = x

The middle integer = x + 1

The largest integer = x + 2

Remark

The first phrase up to is says the sum of ... The key word is sum. So far you have x + x + 1 + x + 2. Simplified this comes to 3x + 3.

Two times the 2nd number is 2*(x + 1) and from that, subtract 14

2(x + 1) - 14

If you break down each phrase as I have done you will soon become very good at doing these types of problems.

So the equation looks like this.

Solution

3x + 3 = 2(x + 1) - 14 Remove the brackets.

3x + 3 = 2x + 2 - 14 Combine the like terms on the right.

3x + 3 = 2x - 12 Subtract 3 from both sides.

3x = 2x - 12 - 3

3x = 2x - 15 Subtract 2x from both sides.

3x - 2x = - 15

x = -15 <<<< Answer for smallest number.

Answer

-15

- 14

-13 Are the three numbers you seek.