Respuesta :
Answer:
2 < x < 6.
Step-by-step explanation:
3.5x-10 > -3
3.5x > 7
x > 2.
8x - 9 < 39
8x < 48
x < 6.
Answer:
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
∵ [tex]\frac{1}{3.5}[/tex] and [tex]\frac{1}{8}[/tex] are positive numbers
Thus, after multiplying by these numbers the inequalities sign do not change,
i.e. [tex]x> \frac{7}{3.5}[/tex] and [tex]x< \frac{48}{8}[/tex]
⇒ x > 2 and x < 6
⇒ 2 < x < 6
