Question

16 plus 5 times a number is more than the number minus 8. Write an inequality and solve it

Answer 1

n > -6 is the inequality for 16 plus 5 times a number is more than the number minus 8

Solution:

Given statement is:

16 plus 5 times a number is more than the number minus 8

We have to write a inequality

From given statement,

16 plus 5 times a number is more than the number minus 8

Let the number be "n"

Therefore,

16 plus 5 times "n" is more than "n" minus 8

Here, "plus" means addition and "minus" means subtraction and "times" means multiplication

Thus the statement is translated into inequality as:

$16 + 5n >n-8$

Simplify the inequality

$16 + 5n >n-8\\\\\mathrm{Subtract\:}16\mathrm{\:from\:both\:sides}\\\\16 + 5n -16 > n - 8 -16\\\\5n >n-24\\\\\mathrm{Subtract\:}n\mathrm{\:from\:both\:sides}\\\\5n-n>n-24-n\\\\\mathrm{Simplify}\\\\4n>-24\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\\\frac{4n}{4}>\frac{-24}{4}\\\\n>-6$

Thus the soultion is n > -6