Find the range of values of $x : | 4 x - 3 | - 9 < 0$

1.5 \leq x \leq 3

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x < 3

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x < 1.5

x > 3

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x \leq - 3

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- 1.5 < x < 3

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Solution

The correct option is E $- 1.5 < x < 3$
Given, $∣ 4 x - 3 ∣< 9$
$\Rightarrow 4 x - 3 + 3 > - 9 + 3$
$\Rightarrow 4 x > - 6$
$\Rightarrow x > - 1.5$
And $∣ 4 x - 3 ∣< 9$
$\Rightarrow 4 x - 3 + 3 < 9 + 3$
$\Rightarrow 4 x < 12$
$\Rightarrow x < 3$
Then $- 1.5 < x < 3$

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