Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.)...

Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1) 5.) (m – 7)( –3) 6.) –12(3 + n)

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Transcript of Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.)...

Warm-up

Use the distributive property to rewrite the expression without parentheses.1.) 8(x + 5) 2.) 4(y – 7) 3.) (x – 4)(2)

4.) –6(r – 1) 5.) (m – 7)( –3) 6.) –12(3 + n)

Warm-up continued

7.) (x)(x + 3) 8.) (–a)(a + 3) 9.) (2x + 1)(5x)

Page 3: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Algebra 1Unit 1

Section 1.5 Notes: Equations

Page 4: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Open Sentence: a mathematical statement with one or more variables.Equation: a mathematical sentence that contains an equals sign, =.

Page 5: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Solving an open sentence: Finding a replacement value for the variable that results in a true sentence or an ordered pair that results in a true statement when substitute into the equation.

Solution: a replacement value for the variable in an open sentence.

Replacement Set: a set of numbers from which replacements for a variable may be chosen.

Page 6: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Set: a collection of objects or numbers that is often shown using braces.

Element: Each object or number in the set.

Solution Set: the set of elements from the replacement set that make an open sentence true.

Page 7: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Example 1

a) Find the solution set of the equation if the replacement set is {2, 3, 4, 5, 6}.

Page 8: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Example 1 Continued

b) Find the solution set of the equation if the replacement set is {0, 1, 2, 3}.

You can often solve an equation by applying the order of operations.

Page 9: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Example 2

a) Solve

a. 19 b. 27 c. 33 d. 42

b) Solve

a. 3 b. 6 c. 14.2 d. 27

Page 10: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Example 3: Solve each equation.

Some equations have a unique solution. Other equations do not have a solution.

Page 11: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Example 4

Identity: an equation that is true for every value of the variable.Solve

Page 12: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Example 5

a) Dalila pays $16 per month for a gym membership. In addition, she pays $2 per Pilates class. Write and solve an equation to find the total amount Dalila spent this month if she took 12 Pilates classes.

Page 13: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Example 5 Continued

b) Amelia drives an average of 65 miles per hour. Write and solve an equation to find the time it will take her to drive 36 miles.

Page 14: Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.) 4(y – 7)3.) (x – 4)(2) 4.) –6(r – 1)5.) (m – 7)( –3)

Exit Slip

Complete problems #2, 5, 8, 11, & 12 in your workbook. Raise your hand when you finish and I’ll come by to check your answers

FRAGATA BERGANTIN GALEÓN CRUCERO DRAGÓN · FRAGATA 401 BERGANTIN 303 CRUCERO 106: 22 X = X = X = 4 4 4 3:18 X = X = X = 5 4 6 9: 21 X = X = X = 8 4 3 9: 39 X = X = X = 4 1 6 2:

Use properties of real numbers to write the expression 5( x + q ) without parentheses. Select the correct answer. 1234567891011121314151617181920 2122232425262728293031323334353637383940.

Distribute: 3(x + 4) = 3(x – 4) = -3(x – 4) = -3(x + 4) =

$Annalisa Scarrone - Bollemusicamidi.altervista.org/alterpages/files/AnnalisaScarrone-Bolle.pdfTrack 1 Track 2 Track 4 a b a 4 4 4 4 4 4 X X X X X X X X X MIDI X ç H G Û \ IH G by93peppe-G$

Annalisa Scarrone - Bollemusicamidi.altervista.org/alterpages/files/AnnalisaScarrone-Bolle.pdfTrack 1 Track 2 Track 4 a b a 4 4 4 4 4 4 X X X X X X X X X MIDI X ç H G Û \ IH G by93peppe-G

Parentheses Nº5 / Paolo Parisi / Via di Soffiano, Firenze

PARENTHESES – {[( )]} EXPONENTS MULTIPLICATION or...P E MD AS ORDER OF OPERATIONS AGREEMENT PARENTHESES – If there are grouping symbols (parentheses, brackets, braces – {[( )]},

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$Removing Parentheses - Humboldt State University · \Kvant" (\Quantum" in Russian) ... A typical issue of Kvant consisted of four feature articles, two in ... Removing Parentheses$

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Parentheses n°1

Uniparental functionalX Turner retardation Xmar(X)/r(X) chromosomes were notalwaysshownbythe Giemsa banding, the secondallele ofthe chromosome is shownin parentheses whenthe polymorphic

Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.)...

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Transcript of Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5)2.)...