12/5/11 §Bellringer: l What is the greatest common factor of 30 and 45? l If you did not finish your test, fill out your agenda to come back for E&R tomorrow!

Equations

Whatever you do to an equation, do the SAME thing to BOTH sides of that equation! Start with adding/subtracting then do multiplying/dividing. (Reverse order of operations) To get a number to cross out, do the opposite operation. You are trying to get x by itself to see what it equals!

Solve this equation for x: x + 3 = 8

Check: x + 3 = = 8 8 = 8 true

Solve for x. x-4=10 5x=25 X = 10 4

# To 6:40

Solve this equation for x: 5x - 2 = 13

Check: 5x - 2 = 13 5(3) - 2 = = = 13 true

2x – 4 = 8

5x + 10 = 80

-3x – 4 = -82

12/6/11 §Get out your homework! §Bellringer: l Add WITHOUT A CALCULATOR!!! (-4) 4+(-6) 5+(-2)

Homework Answers 1.x=4 2.k=12 3.n=12 4.z=6

2/3x + 2 = 8

x/5 + 2 = 8

Worksheet

Get the goof- What did the person do wrong? Solve for x: 4x+12= x12= x = 6

Writing Equations Add- more than, increases by, sum Subtract- less, less than, difference, decreases by Multiplication- product, twice, times Division-quotient Equals- is Write in order of the words EXCEPT when it says less than! Switch the order for less than!

Worksheet Write into an equation and then solve. 1.Four more than twice a number is 8 3. Five less than twice a number is 7

15. Eight more than the quotient of a number and 5 is 3

Video # 6:40

Solve this equation for x: 4x + 5 = x - 4

Check: 4x + 5 = x - 4 4(-3) + 5 = = = -7 true

7y y + 1 = 2y + 2

Check: 7y y + 1 = 2y + 2 7(-2) (-2) + 1 = 2(-2) = = -2 true

3(n - 1.8) = 2n + 1

Check: 3(n - 1.8) = 2n + 1 3( ) = 2(6.4) + 1 3(4.6) = = 13.8 true

An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: < : less than ≤ : less than or equal to > : greater than ≥ : greater than or equal to

Inequalities Solve the exact same way, but it has a instead of = If you multiply or divide by a negative number, switch the sign! When graphing, are open circles and ≤ and ≥ are closed circles. Color everything x could be.

“x < 5” means that whatever value x has, it must be less than 5. Try to name ten numbers that are less than 5!

Numbers less than 5 are to the left of 5 on the number line If you said 4, 3, 2, 1, 0, -1, -2, -3, etc., you are right. There are also numbers in between the integers, like 2.5, 1/2, -7.9, etc. The number 5 would not be a correct answer, though, because 5 is not less than 5.

“x ≥ -2” means that whatever value x has, it must be greater than or equal to -2. Try to name ten numbers that are greater than or equal to - 2!

Numbers greater than -2 are to the right of 5 on the number line If you said -1, 0, 1, 2, 3, 4, 5, etc., you are right. There are also numbers in between the integers, like -1/2, 0.2, 3.1, 5.5, etc. The number -2 would also be a correct answer, because of the phrase, “or equal to”. -2

Examples Graph x > 7 Graph -4 ≥ x Since the sign is >, we put an OPEN circle on 7. X is greater than 7 so we color up the number line. Since the sign is ≥ we put a CLOSED circle on -4. X is smaller than -4 so we color down the number line.

Solving One-Step Inequalities

6) Solve x -14 < 16 x - 14 < x < = = 16 Solve this problem like an equation 1.Draw “the line” 2.Add 14 to both sides 3.Simplify 4.Check your answer 5.Graph the solution o

8) Solve 8y + 3 > 9y - 14 o y - 8y 3 > y > y y < 17 8(17) + 3 = 9(17) Draw “the line” 2.Subtract 8y from both sides 3.Simplify 4.Add 14 to both sides 5.Simplify 6.Rewrite inequality with the variable first 7.Check your answer 8.Graph the solution

Solve for x: ( x / 3 ) > -4 Solve for x: 6x > 36

Inequalities If you multiply or divide by a negative number, the sign changes!

Examples of when to switch signs -3x+4 > 21 X – 7 < 45 -2

Solving One-Step Inequalities

Writing Inequalities You have at least 35 minutes to complete your quiz. The speed limit is 55 mph. At the most, you can spend $50.

Worksheet

Metropolis Gas and Power charges their customers a monthly service charge of $13.60 and a volume charge of $1.59 for every 100 cubic feet of natural gas used. Which of the following equations could be used to find Bruce Wayne's monthly gas bill? (Let x represent the number of cubic feet of gas used in hundreds and y represent the total monthly cost.)

7 - x < 6 What is the first step when solving the equation for x? ( 1 / 5 ) (6x + 4) = 4x Solve for x. x / = 5

Study Island Click on Nolan Period ____ Click on equations. Complete 10 questions in test mode. When you finish with equations work on Inequalities. Turn scratch paper into basket. This is a grade!!!! Test on Monday!