Question

Solve the inequation:
2|4 – 5x| ≥ 9

Answer 1

2|4 – 5x| ≥ 9

∴ `|4 - 5"x"| ≥ 9/2`

∴ `4-5"x"≥9/2` or `4-5"x"≤-9/2` .....[|x| ≥ a implies x ≤ − a or x ≥ a]

Subtracting 4 from both sides, we get

`-5"x"≥1/2` or `-5"x"≤-17/2`

Divide by − 5 (so inequality sign changes)

∴ `"x"≤-1/10` or `"x"≥17/10`

∴ x takes all real values less than or equal to `-1/10` or it takes all real values greater or equal to `17/10`.

∴ the solution set is `[−∞,-1/10]` or `[17/10,∞]`