Presentation on theme: "Chapter 3 Solving Equations"— Presentation transcript:
1 Chapter 3 Solving Equations Introduction to EquationsEquation: equality of two mathematical expressions. =9 + 3 = 123x – 2 = 10y² + 4 = 2y - 1
2 Solution to an equation, is the number when substituted for the variable makes the equation a true statement.Is –2 a solution or 2x + 5 = x² - 3 ?Substitute –2 in for the x2(-2) + 5 = (-2)² - 3= 4 - 31 = 1
3 Solve an equation Addition Property r – 6 = We use the Additionmethod by addingpositive 6 to both sidesof the equation.r = 20*CHECK your solution
4 Solve an equations + ¾ = ½- ¾ -¾ Using the AdditionMethod add a negative¾ to both sides.s = -¼ Remember to get a commondenominator.Check your solution.
5 Solving Equations3y = 27Using the MultiplicationMethod we divide by the coefficient, which is the same as multiplying by ⅓3y = 27y = 9Check your solution
6 Solving EquationsUsing the multiplicationmethod we multiply thereciprocal of thecoefficient to both sides.X = 10Check 4/5(10) = 88 = 8
8 Basic Percent Equations Percent • Base = Amount P • B = A 20% of what number is 30multiplyBequals.2 • B = 30B = 150
9 Basic Percent Equations Percent • Base = Amount P • B = A What Percent of 80 is 70P multiply equalsP • 80 = 70P = .875P = 87.5%Convert to percentage.
10 Basic Percent Equations Percent • Base = Amount P • B = A 25% of 60 is what?multiplyequalsamount.25 • 60 = A15 = A
11 Steps to solve equations: 1. Remove all grouping symbolsLook to collect the left side andthe right side.Add the opposite of the smallestvariable term to each side.Add the opposite of the constantthat’s on the same side as thevariable term to each side.
12 Steps to solve equations continued 5. Divide by the coefficient.*variable term = constant term*if the coefficient is a fraction,multiply by the reciprocal.6. CHECK the solution.
15 Translating Sentences into Equations Equation-equality of two mathematicalexpressions.Key words that mean =equalsisis equal toamounts torepresents
16 Ex. Translate:“five less than a number is thirteen”n - 5=13n = 18Solve
17 Translate Consecutive Integers Consecutive integers are integers thatfollow one another in order.Consecutive odd integers- 5,7,9Consecutive even integers- 8,10,12
18 CHAPTER 4 POLYNOMIALSPolynomial: a variable expressionin which the terms are monomials.Monomial: one term polynomial5, 5x², ¾x, 6x²y³ Not: or 3Binomial: two term polynomial5x² + 7Trinomial: Three term polynomial3x² - 5x + 8
19 Addition and Subtraction Polynomials can be added verticallyor horizontally.Horizontal FormatCollect like termsEx. ( 3x³ - 7x + 2) + (7x² + 2x – 7)3x³+ 7x²- 5x- 5
27 Multiplication of Polynomials Distribute and followRule 1-3a(4a² - 5a + 6)-12a³+ 15a²- 18a
28 Multiplication of two Polynomials *when multiplying two polynomialsyou will use Distributive Property.*be sure every term in one parenthesisis multiplied to every term in theother parenthesis.
29 Multiplication of two Polynomials Ex.(y – 2)(y² + 3y + 1)Multiply y toevery term.Multiply –2 toy³+ 3y²+ y- 2y²- 6y- 2Combine liketerms.y³ + y² - 5y - 2
30 Multiply two Binomials The product of two binomials can befound using the FOIL method.F First terms in each parenthesis.O Outer terms in each parenthesis.I Inner terms in each parenthesis.L Last terms in each parenthesis.
32 Special Products of Binomials Sum and Difference of two Binomials(a + b)(a – b)Square the first termSquare the secondterma²-b²Minus sign between the products
33 Sum and Difference of Binomials (2x + 3)(2x – 3)Square the term 2x-4x²9Square the term 3Minus sign between the terms
34 Or use the short cut Square of a Binomial (a + b)² = (a + b)(a + b) Then FOILOr use the short cut(a + b)² =a²+ 2ab+ b²1. Square 1st term2. Multiply termsand times by 2.ab times 2 =3. Square 2nd term
35 Square of a BinomialEx. (5x + 3)² =25x²+ 30x+ 9Square 5xMultiply 5x and 3then times by 2Square the 3
36 Square of a Binomial (4y – 7)² = 16y² - 56y + 49 Square the 4y Mutiply the 4y and 7then times by 2Square the 7
37 Integer Exponents Divide Monomials x•x•x•x•xx•xx³==Rule 4 xmxnWhen m > nXm-n=xmxn1xn-mWhen n > m=
39 Integer Exponents Zero and Negative Exponents Rule 5 a0 = a ≠ 0x³= x3-3= xº*Summary any number (except for 0) or variable raised to the power of zero = 1
40 Integer Exponents Zero and Negative Exponents x-n =1xnRule 6:1X-n= xnand11If we make everything a fraction,we can see that we take the base and it’s negative exponent and move them from the numerator to the denominatorand the sign of the exponent changes.
41 Integer Exponents Zero and Negative Exponents 25a-4= 2a45