Question

How do you solve and write the following in interval notation: `4x < 2x + 1 ≤ 3x + 2`?

Answer 1

Half closed interval: [-1, 1/2)

Explanation:

Separate solving into 2 parts:
a. 4x < 2x + 1
2x < 1
`x < 1/2`
b. `2x + 1 <= 3x + 2`
`2x - 3x <= 2 - 1`
`- x <= 1`
`x >= -1`
Solution set: Half closed interval: [-1, 1/2)
Graph on the number line:

---------------------- - 1 ========== 0 ==== 1/2 ---------------