Consider the functions g(x) = 6x + 7 and h(x) = 3x - 2. find {x: g(x) > h(x)}

The solution set is x ∈ ( -3 , ∞ ) .

Step-by-step explanation:

Two functions are given to us. And we have to find x such that g(x) > h(x) that is { x : g(x) > h(x)} .

So , the given functions are ,

According to Question ,

⇒ g(x) > h(x)

⇒ 6x + 7 > 3x - 2

⇒ 6x - 3x > -2 -7

⇒ 3x > -9

⇒ x > (-9)/3

⇒ x > (-3)

Hence x can have all values greater than (-3). Therefore x ∈ (-3 , ∞ ) .