Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
1 answer:
You might be interested in
<h2>Answer:</h2>
The question in this problem is:
<em>The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?</em>
<em />
First of all, let's name the first variable which is the smaller number. Accordingly, the lager number will be
given that those numbers are consecutive. On the other hand<em> at most </em>conveys the idea of an inequality, which is:
So:
1. The sum of 2 consecutive integers can be written as:
2. Nine times the smaller and 5 times the larger can be written as:
Finally, the whole statement:
The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:
The two numbers are:
Answer:
Step-by-step explanation:
4x - 12 ≤ 16 + 8x
4x - 8x ≤ 16 + 12
- 4x ≤ 28
<em>x ≥ - 7 or [ - 7, ∞ )</em>
