Question

Which is the solution set of the compound inequality 3.5x-10 >-3 and 8x-9<39?
-2

Answer 1

2 < x < 6.

Explanation:

3.5x-10 > -3

3.5x > 7

x > 2.

8x - 9 < 39

8x < 48

x < 6.

Answer 2

2 < x < 6 or x ∈ (2, 6)

Explanation:

Given compound inequality,

3.5x - 10 > -3 and 8x - 9 < 39,

By using a > b or a < b ⇒ a + c > b + c or a + c < b + c ∀ a, b, c ∈ R,

3.5x > -3 + 10 and 8x < 39 + 9

3.5x > 7 and 8x < 48

∵
`(1)/(3.5)` and
`(1)/(8)` are positive numbers

Thus, after multiplying by these numbers the inequalities sign do not change,

i.e.
`x> (7)/(3.5)` and
`x< (48)/(8)`

⇒ x > 2 and x < 6

⇒ 2 < x < 6