The set $A = {x : | 2 x + 3 | < 7}$ is equal to the set:

B = {x : - 3 < x < 7}

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C = {x : - 13 < 2 x < 4}

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D = {x : 0 < x + 5 < 7}

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E = {x : - 7 < x < 7}

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Solution

The correct option is C $D = {x : 0 < x + 5 < 7}$
First solve the inequality $| 2 x + 3 | < 7$
$\Rightarrow - 7 < 2 x + 3 < 7$
$\Rightarrow - 7 - 3 < 2 x < 7 - 3$
$\Rightarrow - 10 < 2 x < 4$
$\Rightarrow - 5 < x < 2$
$\Rightarrow - 5 + 5 < x + 5 < 2 + 5$ , add 5 each sides
$\Rightarrow 0 < x + 5 < 7$

Hence option 'C' is correct choice

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Similar questions

A = x : | 2 x + 3 | < 7

\int \frac{d x}{(x + 4)^{\frac{8}{7}} (x - 3)^{\frac{6}{7}}}

C

∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} - 2 x + 3 & 7 x + 2 & x + 4 2 x + 7 & x^{2} - x + 2 & 3 x 3 & 2 x - 1 & x^{2} - 4 x + 7 \end{matrix} ∣ ∣ ∣ ∣ ∣ = a x^{6} + b x^{5} + c x^{4} + d x^{3} + e x^{2} + f x + g

g

\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y \sqrt{3}

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