Question

Solution set of the inequation given by -11≤4x-3≤13 is: * (-2,4) [-11,13] [-2,4] [-8,16]​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Solution set of the inequation given by

- 11 ≤ 4x - 3 ≤ 13 is: 

• (-2,4)

• [-11,13]

• [-2,4]

• [-8,16]

EVALUATION

Here the given inequality is

$\sf{ - 11 \leqslant 4x - 3 \leqslant 13}$

Now

$\sf{ - 11 \leqslant 4x - 3 \: \: \: gives}$

$\sf{ \implies \: - 11 + 3 \leqslant 4x }$

$\sf{ \implies \: 4x \geqslant - 8 }$

$\sf{ \implies \: x \geqslant -2 }$

Again

$\sf{ \: 4x - 3 \leqslant 13 \: \: \: gives }$

$\sf{ \implies \: 4x \leqslant 13 + 3}$

$\sf{ \implies \: 4x \leqslant 16}$

$\sf{ \implies \: x \leqslant 4}$

Combining we get

- 2 ≤ x ≤ 4

Hence the required solution set is [ - 2 , 4 ]

FINAL ANSWER

Hence the correct option is [ - 2 , 4 ]

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