Solve the inequation:2|4 – 5x| ≥ 9 - Mathematics and Statistics

Sum

Solve the inequation:
2|4 – 5x| ≥ 9

Solution

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,∞]

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 8 Linear Inequations
Exercise 8.1 | Q 4. (vii) | Page 116