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

2 < x < 6.

Step-by-step explanation:

3.5x-10  > -3

3.5x > 7

x > 2.

8x - 9 < 39

8x < 48

x < 6.

2 < x < 6 or x ∈ (2, 6)

Step-by-step 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

∵ and are positive numbers

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

i.e. and

⇒ x > 2 and x < 6

⇒ 2 < x < 6