Question

Please ans the 1uestion for 20 points

Answer 1

Question :-

Seven times the sum of an integer and 12 is at least 50 and at most 60. Write and solve the inequality and express this relationship.

$\large\underline{\sf{Solution-}}$

Given that,

Seven times the sum of an integer and 12 is at least 50 and at most 60.

Let assume that integer be x.

So,

$\rm \: 7(x + 12) \geqslant 50 - - - (1)$

and

$\rm \: 7(x + 12) \leqslant 60 - - - (2)$

From equation (1) and (2), we concluded that

$\rm \: 50 \leqslant 7(x + 12) \leqslant 60$

can be rewritten as

$\rm \: 50 \leqslant 7x + 84 \leqslant 60$

On Subtracting 84 from each term, we get

$\rm \: 50 - 84 \leqslant 7x + 84 - 84 \leqslant 60 - 84$

$\rm \: - 34 \leqslant 7x \leqslant - 24$

On dividing by 7, each term we get

$\rm \: - \dfrac{34}{7} \leqslant x \leqslant - \dfrac{24}{7}$

$\rm\implies \:x \: \in \: \bigg[- \dfrac{34}{7}, \: - \dfrac{24}{7} \bigg]$

As it is given that, x is an integer.

$\rm\implies \:x \: = \: \{ - 4\}$

$\rule{190pt}{2pt}$

Additional Information :-

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