# 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

Sep 4, 2017

#### Answer:

#### 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#