Question

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"`

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`