Question

Which of the following graphs is the solution set of −10<3x−4<8?

a) 3≤x<4
b) x≤−2
c) [infinity]
d) −2

Answer 1

The solution set for the inequality -10 < 3x - 4 < 8 can be found by solving each inequality separately and then intersecting the solution sets. The correct graph is 3 ≤ x < 4.

Step-by-step explanation:

The solution set for the inequality −10<3x−4<8 can be found by solving each inequality separately and then intersecting the solution sets.

First, let's solve the inequality 3x−4<8:

Add 4 to both sides: 3x<12

Divide both sides by 3: x<4

Next, let's solve the inequality −10<3x−4:

Add 4 to both sides: −6<3x

Divide both sides by 3: −2<x

Intersecting the solution sets, we find that the correct graph is a) 3≤x<4.