Question

Solve: `(3x)/5 + 2 < x+4<= x/2 + 5, x ∈ R` and represent the solution set on the number line.

Answer 1

1) `(3x)/5 + 2 < x + 4 (3x)/5 + 2 < x + 4 `

⇒ `2 - 4 < x - (3x)/5 = (2x)/5`

⇒ `-2 < (2x)/5`

⇒ −10 < 2x

⇒ x > −5

2) `x + 4 ≤ x/2 + 5 x - x/2 ≤ 5 - 4 (1/2)x ≤ 1 x ≤ 2`

Combine: x > −5 and x ≤ 2

−5 < x ≤ 2