Question

For the inequation, `4x - 19< (3x)/5 -2 <= -2/5 + x, x ∈ R` the solution set is ______.

Options

• −4 < x < 5

• −4 < x ≤ 5

• −4 ≤ x < 5

• −4 ≤ x ≤ 5

Answer 1

For the inequation, `4x - 19< (3x)/5 -2 <= -2/5 + x, x ∈ R` the solution set is −4 ≤ x < 5.

Explanation:

`4x − 19 < (3x)/5 − 2`

Multiply by 5:

20x − 95 < 3x − 10

17x < 85

x < 5

`(3x)/5 − 2 ≤ −2/5 + x`

Multiply by 5:

3x − 10 ≤ −2 + 5x

−2x ≤ 8

x ≥ −4

Combine:

−4 ≤ x < 5