Question

3x - 4 > 5 and 4x - 1 < 2. Use interval notation to express the solution.

a. x in (-[infinity], 1)
b. x in (-[infinity], -1)
c. x in (-[infinity], 0)
d. x in (-[infinity], -3)

Answer 1

To solve the system of inequalities, we isolate x in each inequality and find the overlapping solution. The solution in interval notation is x in (3, 0.75).

Step-by-step explanation:

To solve the system of inequalities, we need to find the values of x that satisfy both inequalities.

1. Solving the first inequality, 3x - 4 > 5, we add 4 to both sides and then divide by 3 to isolate x. This gives us x > 3.
2. Solving the second inequality, 4x - 1 < 2, we add 1 to both sides and then divide by 4 to isolate x. This gives us x < 0.75.

So the solution to the system of inequalities is x > 3 and x < 0.75. In interval notation, this can be expressed as x in (3, 0.75).