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"?

Answer 1

#"see explanation"#

#"let n be the number"#
#"then the sum of this number and 7 is "n+7#
#"and 3 times this sum is "3(n+7)#
#"5 times the number less thirteen is "5n-13#
#rArr3(n+7)>5n-13larrcolor(red)" is the inequality"#
#"distribute the brackets on the left side"#
#3n+21>5n-13#
#"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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Answer 2

To write the inequality and solve the given statement "three times the sum of a number and seven is greater than five times the number less thirteen," it can be expressed as:

3(x + 7) > 5x - 13

To solve:

3x + 21 > 5x - 13 21 + 13 > 5x - 3x 34 > 2x x < 17

Therefore, the solution to the inequality is x < 17.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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