Write an inequality and solve each problem.

25. Five less than a number is at least - 2.

26. The difference between a number and 6 is no more than 5.

27. The sum of a number and 7 is more than 1.

28. The difference between a number and ten is greater than 9.

29. Four less than a number is less than 11.

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