Question

Write an inequality and solve each problem.

Answer 1

For all of these, let n = the unknown number. 

25) "Five less than a number" becomes 5 - n 
"At least" tells you your number is greater than or equal to - 2.
Put it all together.

5 - n ≥ - 2
- n ≥ - 2 - 5
- n ≥ - 7
Divide by - 1 to isolate the variable. This flips the operation.

n ≤ 7

26) "The difference between a number and 6" tells you to do n - 6
"no more than" means this is a less than or equal to sign. 

n - 6 ≤ 5
n ≤ 5 + 6

n ≤ 11

27) "The sum of a number and 7" becomes n + 7
"more than" is a greater than sign

n + 7 > 1
n > 1 - 7

n > - 6

28) "The difference between a number and 10" becomes n - 10
Obvious one, "greater than" is... just that.

n - 10 > 9
n > 9 + 10

n > 19

29) "Four less than a number" is 4 - n
Another obvious one in "less than" 

4 - n < 11
- n < 11 - 4
- n < 7
Divide by - 1 on both sides to isolate the variable

n > - 7