6.1 Solving Inequalities with adding and subtracting

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# 6.1 Solving Inequalities with adding and subtracting - PowerPoint PPT Presentation

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. o. 1) Graph the solution set of x &lt; 3.

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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

o

1) Graph the solution set ofx < 3.

When you have < or >, use an open dot!

2) Graph the solution set ofy ≥ -5/4.

When you have ≤ or ≥, use a closed dot!

Converting -5/4 to a decimal = -1.25

o

3) Graph the solution set ofp ≠ 2.

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

o

29

30

31

6) Solve x + (-14) < 16
• Solve this problem like an equation
• Draw “the river”
• Eliminate double signs
• Add 14 to both sides
• Simplify Set Notation
• Graph the solution

x- 14< 16

+ 14 + 14

{x|x < 30}

30 + (-14) = 16

16 = 16

-15

-14

-13

7) Solve y + 21 ≥ 7
• Draw the “river”
• Subtract 21 from both sides
• Simplify in Set Notation
• Graph the solution

- 21 -21

{y|y≥ -14}

(-14) + 21 = 7

7 = 7

o

16

17

18

8) Solve 8y + 3 > 9y - 14

- 8y - 8y

3 > y - 14

+ 14 + 14

17 > y

{y|y < 17}

8(17) + 3 = 9(17) - 14

• Draw “the river”
• Subtract 8y from both sides
• Simplify
• Add 14 to both sides
• Simplify
• Rewrite inequality in Set Notation
• Graph the solution

o

6

7

8

o

6

7

8

6

7

8

6

7

8

9) What is the graph of 7 ≤ m?

30

31

32

- 2r - 2r

r – 17 ≥ 14

+ 17 + 17

{r|r ≥ 31}

3(31) - 17 = 2(31) + 14

• Draw “the river”
• Subtract 2r from both sides
• Simplify
• Add 17 to both sides
• Simplify in Set Notation
• Graph the solution

### 10) Solve 3r - 17 ≥ 2r + 14

11) Solve -2x + 6 ≥ 3x - 4
• {x|x ≥ -2}
• {x|x ≤ -2}
• {x|x ≥ 2}
• {x|x ≤ 2}