Question

Of the following sets, which numbers in {1, 2, 3, 4, 5} make the inequality 5x + 2 > 12 true?

{1, 2}

{1, 2, 3}

{3, 4, 5}

{2, 3, 4, 5}

Answer 1

(3,4,5)

Using 1 you get, 7>12
Using 2 you get, 12>12
Using 3 you get, 17>12
Using 4 you get, 20>12
Using 5 you get, 27>12

this is why only 3,4, and 5 work.

Answer 2

{ 3, 4, 5 }

Explanation:

Given inequality,

5x + 2 > 12

By subtracting 2 on both sides,

5x > 12 - 2

5x > 10

Since,
`(1)/(5)>0`

Thus, after multiplying both sides of inequality by 1/5, the sign of inequality will not change,

That is,

`(5x)/(5) > (10)/(5)`

`x > 2`

⇒ x ∈ ( 2, ∞ )

Hence, numbers in set { 1, 2, 3, 4, 5} that make the given inequality true are,

{ 3, 4, 5 }