solving inequalties (adding & subtracting) james saltmarshall & e’lyse vaughn

Solving inequalTiesSolving inequalTies(adding & subtracting)(adding & subtracting)

JAMES SALTMARSHALLJAMES SALTMARSHALL

&&

E’LYSE VAUGHNE’LYSE VAUGHN

BASIC RULES TO ADDING AND BASIC RULES TO ADDING AND SUBTRACTINGSUBTRACTING

STEP# 1 – First solve the equation where the variable is on one side of the STEP# 1 – First solve the equation where the variable is on one side of the sign.sign.

STEP# 2- Next draw a number line where your answer on the other side is STEP# 2- Next draw a number line where your answer on the other side is in the middle.in the middle.

STEP# 3-Then look at the sign to see if the circle is closed or open. STEP# 3-Then look at the sign to see if the circle is closed or open. If the sign is less than or greater than the circle is open. If the sign is less than or greater than the circle is open. If the sign is a less than or equal to and/or the sign is greater than or equal to the circle is If the sign is a less than or equal to and/or the sign is greater than or equal to the circle is

closed.closed.

Practice Problems

X+20 X+20 << 35 35 Y+ 25 Y+ 25 >> 50 50 J + 16 > 32J + 16 > 32 E + 30 < 45E + 30 < 45 20 < v + 1520 < v + 15

A – 60 A – 60 << 10 10 B – 15 > 30B – 15 > 30 C – 20 > 20 K – 20 < 60 5 > d - 5

Summary toolSolve inequalities by adittion and subtraction

T-45 < 13 original inequality t-45 + 45 < 13 + 45 add 45 to each side t < 58 simplify

check – to substitute a number less than 58 , and a number greater than 58

The solution is the set {all numbers less than or equal to 58}

54 55 56 57 58 59

the heavy arrow pointing to the dot at 58 shows that 58 is included left shows that the inequality in the inequality. includes all numbers less than 58

AnswersAnswers

X+20 X+20 << 35 35

-20 -20-20 -20

x x << 15 15

14 15 1614 15 16

Y+ 25 Y+ 25 >> 50 50

- 25 -25- 25 -25

y y >> 25 25

24 25 2624 25 26

J + 16 > 32J + 16 > 32

- 16 -16- 16 -16

j > 16j > 16

15 16 1715 16 17

E + 30 < 45E + 30 < 45

- 30 -30- 30 -30

e < 15e < 15

14 15 1614 15 16

20 < v + 1520 < v + 15

-15 - 15-15 - 15

5 < v5 < v

4 5 64 5 6

SubtractingSubtracting A – 60 A – 60 << 10 10

+ 60 +60+ 60 +60

a a << 70 70

69 70 7169 70 71

B – 15 > 30B – 15 > 30

+ 15 + 15+ 15 + 15

b > 45b > 45

44 45 4644 45 46

C – 20 > 20 +20 +20 c > 40

39 40 41

K – 20 < 60 +20 +20 k < 80

79 80 81

5 > d-5 +5 +5 10 > d

9 10 11

resources

http://www.math-play.com/InequalityGame.html

http://www.purplemath.com/modules/ineqsolv2.htm

www.algebra1.com