Question

Find the first of three consecutive even integers if the sum of the first and second is 15 less than 3 times the third.

Answer 1

Answer:

First even integer: 6

Step-by-step explanation:

Inequalities

Assume x is the first even integer. The next integer is x+2, and the last integer ix x+4.

The condition states that the sum of the first and the second number is 15 less than three times the third. This takes us to the inequality:

$x+x+2$

Operating:

$2x+2$

Subtracting 2 and 2x:

$0$

Simplifying:

$0$

Solving:

x>5

There are infinitely many solutions. For example, for x=6 (first even number into the solution interval):

First integer: 6

Second integer: 8

Third integer: 10

There are other solutions, like 20,22,24 but the first set is 6,8,10.