Question

Solve -7 < 4x + 1 = 23, x E I.​

Answer 1

SOLUTION

TO SOLVE

- 7 < 4x + 1 < 23 where x ∈ I

EVALUATION

Here the given inequality is

$\sf{ - 7 < 4x + 1 < 23}$

Now I is the set of integers

Now we solve the inequality

$\sf{ - 7 < 4x + 1 < 23}$

$\implies \: \sf{ - 7 - 1< 4x + 1 - 1 < 23 - 1}$

$\implies \: \sf{ - 8 \: < 4x < 22}$

$\displaystyle \implies \: \sf{ - \frac{8}{4} \: < \frac{4x}{4} < \frac{22}{4} }$

$\displaystyle \implies \: \sf{ - 2 \: < x < \frac{11}{2} }$

$\displaystyle \implies \: \sf{ - 2 \: < x < 5.5 }$

Since x is an integer

x = - 1 , 0 , 1 , 2 , 3 , 4 , 5

Hence the solution set

S = { - 1 , 0 , 1 , 2 , 3 , 4 , 5 }

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