For how many integers, a, is it true that 2

Question

For how many integers, a, is it true that 2 < |a| < 9?

A 4
B 5
C 6
D 10
E 12

Chethan92 · Answer

|a| is always positive.
a can take 3,4,5,6,7,8 and -3,-4,-5,-6,-7,-8.
Total 12 values.

E is the answer.

KSBGC · Answer

Given,

2 < |a| < 9

**** |a| yields positive integers.

So, we must consider both positive and negative integers withing this range.

a = 3 , 4, 5, 6 , 7 , 8.

a = -3, -4, -5, -6, -7 , -8

Total: 12 integers.

E is the correct answer.

Archit3110 · Answer

2 < |a| < 9
lal = for both + & -ve (3,4,5,6,7,8)

total 12 IMO E

Lowpoint · Answer

To find the number of terms between two numbers in a set of consecutive integers we can use the formula:
Last Number - First Number - 1

So here it's 9-2-1 = 6. So there are a total of 6 numbers between 2 and 9.

We know that absolute values include positive and negative integers. So we need to double the result by multiplying the number of terms with 2 so 6*2 =12.

Answer: E

BrushMyQuant · Answer

We need to find For how many integers, a, is it true that 2 < |a| < 9?

As we have \|a\| in the equation so we will have two cases
-Case 1: a ≥ 0 => \|a\| = a => 2 < a < 9 => Possible integer values of a are from 3 to 8 => (8-3) + 1 => 6 values	-Case 2: a ≤ 0 => \|a\| = -a => 2 < -a < 9 Multiplying with -1 on all the sides and changing the sign of the inequality => -2 > a > -9 => -9 < a < -2 => Possible integer values of a are from -8 to -3 => 6 values

=> We have total 6 + 6 = 12 solutions

So, Answer will be E
Hope it helps!

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For how many integers, a, is it true that 2 < |a| < 9?

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