Question

How do you write an inequality and solve given "seven tenths of a number plus 14 is less than forty nine"?

Answer 1

`x<50`

Explanation:

`"let the number be "x`

`rArr7/10x+14<49larr" is the inequality to be solved"`

`"to eliminate the fraction, multiply ALL terms by 10"`

`cancel(10)xx7/cancel(10) x+(10xx14)<(10xx49)`

`rArr7x+140<490`

`"subtract 140 from both sides"`

`7xcancel(+140)cancel(-140)<490-140`

`rArr7x<350`

`"divide both sides by 7"`

`(cancel(7) x)/cancel(7)<350/7`

`rArrx<50`

`color(blue)"As a check"`

`"Select a value for " x < 50 ," say 40"`

`rArr7/10xx40+14=28+14=42 < 50color(red)" true"`