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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 of x < 3.

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6 1 solving inequalities with adding and subtracting
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

1 graph the solution set of x 3

o

1) Graph the solution set ofx < 3.

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

2 graph the solution set of y 5 4

2) Graph the solution set ofy ≥ -5/4.

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

Converting -5/4 to a decimal = -1.25

3 graph the solution set of p 2

o

3) Graph the solution set ofp ≠ 2.

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

6 solve x 14 16

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
  • Check your limit
  • Graph the solution

x- 14< 16

+ 14 + 14

{x|x < 30}

30 + (-14) = 16

16 = 16

7 solve y 21 7

-15

-14

-13

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

- 21 -21

{y|y≥ -14}

(-14) + 21 = 7

7 = 7

8 solve 8 y 3 9 y 14

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
  • Check your limit
  • Graph the solution
9 what is the graph of 7 m

o

6

7

8

o

6

7

8

6

7

8

6

7

8

Answer Now

9) What is the graph of 7 ≤ m?

10 solve 3r 17 2r 14

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
  • Check your limit
  • Graph the solution

10) Solve 3r - 17 ≥ 2r + 14

11 solve 2x 6 3x 4

Answer Now

11) Solve -2x + 6 ≥ 3x - 4
  • {x|x ≥ -2}
  • {x|x ≤ -2}
  • {x|x ≥ 2}
  • {x|x ≤ 2}
12 joanna s tests were 87 93 88 and 94 what must her 5th grade be to get a total of at least 459

Answer Now

12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a total of at least 459?
  • 96
  • 97
  • 98
  • 100