graph inequalities on a number line.

1
6.1 Solving Inequalities with adding and
subtracting

• graph inequalities on a number line.
• solve inequalities using addition and
  subtraction.
• SOL A.1, A.3

Designed by Skip Tyler, Varina High School Edited
by Eddie Judd, Crestwood Middle School
2
1) Graph the solution set ofx lt 3.

• When you have lt or gt, use an open dot!

3
2) Graph the solution set ofy -5/4.

• When you have or , use a closed dot!
• Converting -5/4 to a decimal -1.25

4
3) Graph the solution set ofp ? 2.

• When you have ?, use an open dot and shade both
  ways!

5
4) Which inequality would have a closed dot on
the number line?

1. gt
2. lt
4. ?

6
5) Which inequality does NOT use an open dot on
the number line?

2. lt
3. gt
4. ?

7
6) Solve x (-14) lt 16

• x - 14 lt 16
• 14 14
• xx lt 30
• 30 (-14) 16
• 16 16

• Solve this problem like an equation
• Draw the river
• Eliminate double signs
• Add 14 to both sides
• Simplify Set Notation
• Check your limit
• Graph the solution

8
7) Solve y 21 7

• - 21 -21
• yy -14
• (-14) 21 7
• 7 7

1. Draw the river
2. Subtract 21 from both sides
3. Simplify in Set Notation
4. Check your limit
5. Graph the solution

9
8) Solve 8y 3 gt 9y - 14
- 8y - 8y 3 gt y - 14
14 14 17 gt y
yy lt 17 8(17) 3 9(17) - 14

1. Draw the river
2. Subtract 8y from both sides
3. Simplify
4. Add 14 to both sides
5. Simplify
6. Rewrite inequality in Set Notation
7. Check your limit
8. Graph the solution

10
9) What is the graph of 7 m?

?
11
10) Solve 3r - 17  2r 14
- 2r - 2r r 17 14
17 17 rr 31 3(31) -
17 2(31) 14

1. Draw the river
2. Subtract 2r from both sides
3. Simplify
4. Add 17 to both sides
5. Simplify in Set Notation
6. Check your limit
7. Graph the solution

12
11) Solve -2x 6 3x - 4

1. xx -2
2. xx -2
3. xx 2
4. xx 2

13
12) Joannas tests were 87, 93, 88 and 94. What
must her 5th grade be to get a total of at least
459?

1. 96
2. 97
3. 98
4. 100