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Variable Separable Method

Find the solu...

Question

Find the solution set of $| 2 x - 3 | < 7$ .

{

x : - 5 < x < 2

}

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{

x : - 5 < x < 5

}

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{

x : - 2 < x < 5

}

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{

x : x < - 5 o r x > 2

}

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{

x : x < - 2 o r x > 5

}

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Solution

The correct option is C { $x : - 2 < x < 5$ }
Rule is when $| y | < a$
$\Rightarrow - a < y < a$
Now when $| 2 x - 3 | < 7$ , then
$- 7 < 2 x - 3 < 7$
Adding $3$ and then dividing on both sides,
$\Rightarrow - 7 + 3 < 2 x < 7 + 3$
$\Rightarrow - 4 < 2 x < 10$
$\Rightarrow - 2 < x < 5$

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Similar questions

x^{2}

x^{2}

A = {0}, B = {x : x > 15 and x < 5}

C = {x : x - 5 = 0}, D = {x : x^{2} = 25}

E = {x : x

x^{2} - 2 x - 15 = 0}

x : \frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}, x \neq 3, 5

x \in

- 5 \leq 2 x - 3 < x + 2

\frac{x}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4}

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