1. Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
(For help, go to Lesson 2-5.)
Bell Work #12
Solve each equation.
1. m + 7 = k – 8 = 11
h = = n – 23
Check Skills You’ll Need
2-9

2. Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Solutions
m + 7 – 7 = 5 – 7 k – =
12 – 12 + h = 21 – 12
m + 7 = 5
m = – 2
12 + h = 21
h = 9
6 = n – 23
29 = n
= n –
k – 8 = 11
k = 19
2-9

3. Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Key Concepts
Subtraction Property of Inequality
You can subtract the same number from each side of an inequality
Arithmetic
Algebra c
7 > 4, so 7 – 3 > 4 - ___ 3
If a > b, then a – c > b - ___
6 < 9, so 6 – 2 < 9 - ___ 2
If a < b, then a – c < b - ___ c
2-9

4. Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Key Concepts
Addition Property of Inequality
You can add the same number from each side of an inequality
Arithmetic
Algebra c
7 > 3, so > 3 - ___ 4
If a > b, then a + c > b + ___
2 < 5, so < 5 + ___ 6
If a < b, then a + c < b + ___ c
2-9

5. Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Solve each inequality. Graph the solutions. a.
4 + s < 12
4 + s < 12
4 + s – 4 < 12 – Subtract 4 from each side.
s < Simplify. b.
–16 y – 14
> –
–16 y – 14
> –
– y – Add 14 to each side.
> –
–2 y or y –2 Simplify.
> –
<
Quick Check
2-9

6. Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
You have 6 GB on your computer. The files you have stored on the hard drive occupy at least 2 GB. How much storage space is left for other files? =
storage space available. s
Let
storage space for our files
Words
is less than 
or equal to
plus
total
space
storage space left
Inequality 2 6 +
< –
2 + s 6
< –
2 – 2 + s 6 – 2 Subtract 2 from each side.
< –
s Simplify.
< –
Quick Check
No more than 4 GB are left.
2-9

7. Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Solve –10 < –13 + q.
–10 < –13 + q
– < – q Add 13 to each side.
3 < q Simplify.
Quick Check
2-9

8. Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Solve each inequality.
1. e – g – 6
3. A number q plus the opposite of 5 is less than or equal to 0.
> –
<
e 10
< –
– g
> –
q 5
< –
2-9