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प्रश्न
Solve the following inequation and write the solution set:
13x – 5 < 15x + 4 < 7x + 12, x ∈ R
Represent the solution on a real number line.
उत्तर
13x – 5 < 15x + 4 < 7x + 12, x ∈ R
Take 13x – 5 < 15x + 4
13x < 15x + 9
0 < 2x + 9
– 9 < 2x
`-9/2 < x`
and
15x + 4 < 7x + 12
15x < 7x + 8
8x < 8
x < 1
∴ `-9/2 < x < 1`
i.e – 4.5 < x < 1
∴ Solution set = {x : – 4.5 < x < 1, x ∈ R}
The solution on the number line is as follows:
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