Answer:
The three consecutive integers are:
8, 9, 10
Step-by-step explanation:
Given:
There are three consecutive integers.
Three times the smallest is 14 more than the largest.
To find the three integers.
Solution:
Since the integers are consecutive , so each have a common difference of 1.
For example : -3,-2,-1
Let the integers be = [tex]x,(x+1),(x+2)[/tex]
Three times the smallest is 14 more than the largest can be given as:
[tex]3x=(x+2)+14[/tex]
Simplifying and solving for [tex]x[/tex].
[tex]3x=x+2+14[/tex]
[tex]3x=x+16[/tex]
Subtracting both sides by [tex]x[/tex]
[tex]3x-x=x-x+16[/tex]
[tex]2x=16[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}=\frac{16}{2}[/tex]
∴ [tex]x=8[/tex]
Smallest integer = 8
Next integer = 9
Largest integer = 10
