This document provides examples for solving 16 inequality word problems by adding or subtracting the number being added or subtracted from both sides of the inequality. It explains that for problems where a number is being subtracted, that number should be added to both sides since it is negative, and for problems where a number is being added, that number should be subtracted from both sides since it is positive. The document works through each problem as an example, showing the steps to solve it and obtain the simplified inequality. It concludes by reminding students of the rules for adding and subtracting positive and negative numbers.

1. Justice Adams
Honors Math
3rd Period
10/09/2012
Homework/Inequalities
(From Tennessee Math Connects: Course 2. Glencoe McGraw-Hill pg. 247)
Note: Add or subtract the number that is being added to or subtracted from the unknown (letter symbol) to both sides of the
(in)equation (If the number is positive, that number should be subtracted from both sides. If the number is negative, it should
be added to both sides). Simplify your answer.
ALWAYS read the instructions in your text book or otherwise if you are not familiar with a particular mathematical concept
before attempting to solve a problem…..
Answers to some problems are often given in the back of your text book. Use them to check YOUR answers to those particular
problems and to help YOU solve other similar problems. Never simply copy an answer, even if you are not required to show
your work, as you may be required at some point to show your work.
#11. ˗3 < n – 8 Here, since 8 is negative, or is being subtracted, it is to be added to
+8 +8 both sides.
5<n -8+8 is 0 and cancels itself out. You need NOT write the zero sum.
#12. h – 16 ≤ ˗24 Since 16 is negative, or is being subtracted, it is to be added to both
+ 16 +16 sides.
H ≤ -8 -24+16 is -8 (Subtraction occurs when deriving the sum of a positive
and a negative number. The sum carries the sign of the greater or
highest number, however).
#13. y – 6 ≥ ˗ 13 Since 6 is negative, or is being subtracted, it is to be added to both
+6 + 6 sides.
y ≥ ˗7 -13+6 is -7 (Subtraction occurs when deriving the sum of a positive
and negative number. The sum carries the sign of the greater or
highest number, however.)
#14. 3 ≤ m +1.4 Here, since 1.4 is positive, or is being added, it is to be subtracted
˗1.4 ˗1.4 from both sides.
1.6 ≤ m +1.4-1.4 is 0 and cancels itself out. You need NOT write the zero
sum. 3-1.4 is the same as saying 3.0-1.4.
#15. x + 0.7 > ˗ 0.3 Here, since 0.7 is positive, or is being added, it is to be subtracted
˗ 0.7 ˗ 0.7 from both sides.
x > ˗1 -0.3-0.7 is 1.0 due to the decimal alignment here, although you
need NOT write the .0, as this is understood.
Two negative numbers are to be added, although the
sum of those numbers would be negative.
#16. w - 8 ≥ 5.6 Here, since 8 is negative, or is being subtracted, it is to be added to
+8 +8 both sides.
W ≥ 13.6 -8+8 is 0 and cancels itself out. You need NOT write the zero sum.
To obtain the sum of positive and negative numbers utilizing a standard calculator where the larger number is a
negative, type the smaller number into the calculator first. Hit the minus sign. Then type the larger number and hit
the equal sign. To type a negative number utilizing a calculator with a [+/-] button, type the number and hit this
button once. Note: Any number lacking a negative symbol is understood to be positive. Remember and/or learn the
rules concerning the adding and subtraction of negative numbers and the adding and subtraction of negative
numbers with positive numbers, as you may or may not be allowed to utilize a calculator on some tests and/or
quizzes.