Equations and Inequalities Quick Review Quick guide to solving Equations and Inequalities.
Chapter 3 Multi-Step Equations and Inequalities
description
Transcript of Chapter 3 Multi-Step Equations and Inequalities
Chapter Prerequisite Skills
Chapter 3Multi-Step Equations
andInequalities
Chapter Prerequisite Skills1. Explain what an expression is and what an equation is. Then give one example.
Use the distributive property to write and equivalent variable expression.
3. 8(z – 7)
4. -6(-m + 12)
An expression can be a variable expression or a numerical expression. It is not equal or compared to anything. 2x + 7 or 28 – 7
An equation is a mathematical sentence comparing two expressions. 2x + 7 = 28 – 7
9x - 36 8z – 56
6m – 72
2. 9(x – 4)
5. -10(n – 5) -10n + 50
Chapter Prerequisite Skills
Solve the equation. Check the solution.
11. h ÷ 6 = -8
12. q – 9.6 = 2
-6 -48
11.6
10. x + 13 = 7
13. 65 = -13b -5
Simplify the Expression.
7. 9b – 12b + 3
8. 4(a + 2) + a
4 -3b + 3
5a + 8
6. c + 4 – c
9. 2(2d + 5 + d) 6d +10
Lesson Quiz
Lesson Presentation
Lesson 3.1Solving Two-Step
EquationsSkill Check
Skill Check
2. -77 + 37 =
3. -270 ÷ -4 =
-132
-40
67.5
1. -44 – 88 =
4. 765 • (1 ÷ 765) = 1
Writing Variable Expressions You can solve a real-world problem by creating a verbal model and using it to write a variable expression. A verbal model describes a problem using words as labels and using math symbols to relate the words. The table shows common words and phrases that indicate mathematical operations.
Common Words and Phrases that Indicate Operations
Addition Subtraction Multiplication Division
plusthe sum ofincreased bytotalmore thanadded to
minusthe difference ofdecreased byfewer thanless thansubtracted from
timesthe product ofmultiplied byof
divided bydivided intothe quotient of
Study Strategy
For example: 3x + 7 = -5Subtract 7 from both sides: -7 + 3x + 7 = -5 – 7 Simplify: 3x = -12 Divide each side by 3: 3x ÷ 3 = -12 ÷ 3Simplify: x = -4
When you solve an equation show every step when solving, because these steps are important for diagnosing errors.
Using Subtraction and Division to SolveEXAMPLE 1
SOLUTION
a. 8x + 7 = 47
Solve.
a. 8x + 7 = 47
-7 + 8x + 7 = 47 - 7
x = 5 r = -4
b. 1 = 2r + 9
c. 2 = 6h + 20
b. 1 = 2r + 9c. 2 = 6h + 20
8x = 40
8x/ 8 = 40/ 8
-9 + 1 = 2r + 9 – 9-8 = 2r
-8/2 = 2r/2
h = -3
-20 + 2 = 6h + 20 – 20-18 = 6h
-18/6 = 6h/6
Using Addition and Multiplication to SolveEXAMPLE 2
SOLUTION
a. y/4 – 2 = 1
Solve.
a. y/4 – 2 = 1
2 + y/4 – 2 = 1 + 2
y = 12 d = 15
b. 2 = d/5 - 1
c. 12 = f/2 – 8
b. 2 = d/5 - 1c. 12 = f/2 – 8
y/4 = 3
4(y/4) = (3)4
1 + 2 = d/5 – 1 + 13 = d/5
5(3) = (d/5)5
f = 40
8 + 12 = f/2 – 8 + 8
20 = f/2
2(20) = (f/2)2
Solving an Equation with Negative CoefficientsEXAMPLE 3
SOLUTION
a. 9 – 6a = 45
Solve.
a. 9 – 6a = 45
-9 + 9 – 6a = 45 – 9
a = -6 m = -1
b. 6 – 2m = 8
c. -2 = 5 – n
b. 6 – 2m = 8c. -2 = 5 – n
– 6a = 36
– 6a/-6 = 36/-6
-6 + 6 – 2m = 8 – 6– 2m = 2
– 2m/-2 = 2/-2
n = 7
-5 – 2 = 5 – n – 5
-7 = -n
-7/-1 = -n/-1
Writing and Solving a Two-Step EquationEXAMPLE 4Motorcycle William makes a down payment of 1,100,000 won on a motorcycle costing 2,300,000 won. If no interest is charged, how many monthly payments of 150,000 won must he make until he has finished paying for the motorcycle? Let p represent the number of monthly payments. Write a verbal model.
ANSWER
SOLUTION
William must make 8 monthly payments of 150000 won.
Amount of down payment
+Monthly Payment
• Number of monthly payments, p
= Total Cost of Motorcycle
1100000 + 150000 • p = 2300000
p = 8
– 1100000 + 1100000 + 150000p = 2300000 - 1100000150000p = 1200000
150000p/150000 = 1200000/150000
Lesson Quiz
1. 9b + 8 = 80
2. z/7- 5 = -3
3. -10 = 20 – 6c
b = 8 z = 14c = 5
Solve the equation.
5. Challenge Solve (8 + k)/5 = 3 k = 7
4. 11 – b/6 = 23
b = -72
Closure
• 2.) Asia girl has lived one fourth of her life in S.Korea, one fifth of her life in Thailand, one third of her life in China, and she has been living in Japan for the past 13 years. How old is Asia girl?
• 1.) Explain how you solve the equation
11 – 4p = -1?
Asia girl is 60 years old.
Lesson 3.1 Homework:pp.122-124 Exs. (1, 20, 22, 24, 26, 28, 30, 32, 34, 35abc, 45, 46)Challenge/Bonus 36