How do you write an inequality and solve given "three times the sum of a number and seven is greater than five times the number less thirteen"?

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How do you write an inequality and solve given "three times the sum of a number and seven is greater than five times the number less thirteen"?

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Answer 1 · 2017-09-04T13:37:56

$see explanation$ $"see explanation"$

Explanation:

$let n be the number$ $"let n be the number"$

$then the sum of this number and 7 is n + 7$ $"then the sum of this number and 7 is "n+7$

$and 3 times this sum is 3 (n + 7)$ $"and 3 times this sum is "3(n+7)$

$5 times the number less thirteen is 5 n - 13$ $"5 times the number less thirteen is "5n-13$

$\Rightarrow 3 (n + 7) > 5 n - 13 \leftarrow is the inequality$ $rArr3(n+7)>5n-13larrcolor(red)" is the inequality"$

$distribute the brackets on the left side$ $"distribute the brackets on the left side"$

$3 n + 21 > 5 n - 13$ $3n+21>5n-13$

$subtract 3n from both sides$ $"subtract 3n from both sides"$

$cancel(3n)cancel(-3n)+21>5n-3n-13$

$rArr21>2n-13$

$"add 13 to both sides"$

$21+13>2ncancel(-13)cancel(+13)$

$rArr34>2n$

$"divide both sides by 2"$

$17>nrArrn<17$

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How do you write an inequality and solve given "three times the sum of a number and seven is greater than five times the number less thirteen"?

1 Answer

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