Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–2) Then/Now New Vocabulary Key Concept: Addition Property of Equality Example 1: Solve Equations.

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Splash Screen

Lesson Menu Five-Minute Check (over Lesson 4–2) Then/Now New Vocabulary Key Concept: Addition Property of Equality Example 1: Solve Equations by Adding Key Concept: Subtraction Property of Equality Example 2: Solve by Subtracting Example 3: Real-World Example: Solve by Subtracting

Over Lesson 4–2 5-Minute Check 1 Which gives a correct listing for the expression 4q + 5p – 9 – p + 8q? A.terms: 4q, 5p, –p, 8q B.like terms: 4q, 5p C.constants: 9 D.coefficients: 4, 5, –1, 8,

Over Lesson 4–2 5-Minute Check 2 A.13 + m B.13m C.10m + 3 D.10m Simplify the expression 4m + 6m + 3.

Over Lesson 4–2 5-Minute Check 3 A.25a + 16 B.23a + 16 C.24a D.40 Simplify the expression 24a – a + 16.

Over Lesson 4–2 5-Minute Check 4 A.–21r + 7 B.–11r + 63 C.–3r + 63 D.–3r + 7 Simplify the expression 9(r + 7) – 12r.

Over Lesson 4–2 5-Minute Check 5 A.14x – 12 B.14x – 2 C.14x D.10x Simplify the expression 6(x – 2) + 8x.

Over Lesson 4–2 5-Minute Check 6 A.8x – 6y B.2x C.3x – 2y D.5x – 6y The perimeter of the trapezoid below is 11x – 8y. Write an expression for the measure of the fourth side of the figure.

Then/Now You have already worked with the additive inverse of a number when you subtracted integers. (Lesson 2–3) Solve equations by using the Addition and Subtraction Properties of Equality. Translate verbal sentences into equations.

Vocabulary equation solution solving the equation inverse operation equivalent equation

Concept A

Example 1A Solve Equations by Adding x – 4 = –3Write the equation. A. Solve x – 4 = –3. Check your solution and graph it on a number line. x + 0= 1Additive Inverse Property x=1Identity Property + 4=+ 4Addition Property of Equality

Example 1A Solve Equations by Adding Check x – 4 = –3Write the equation. To check that 1 is the solution, replace x with 1 in the original equation. ? 1 – 4=–3Check to see if the sentence is true. –3= –3The sentence is true. Answer: The solution is 1. Draw a dot at 1 on the number line.

Example 1B Solve Equations by Adding –8.4 = n – 6.1Write the equation. B. Solve –8.4 = n – 6.1. Check your solution and graph it on a number line. –2.3= n + 0Additive Inverse Property –2.3=nIdentity Property + 6.1=+ 6.1Addition Property of Equality Answer: The solution is –2.3. Draw a dot at –2.3 on the number line.

Example 1A A. Solve x – 7 = –3. Graph the solution on a number line. A.x = 10; B.x = –10; C.x = 4; D.x = –4;

Example 1B B. Solve –7.1 = m – 3.8. Graph the solution on a number line. A.x = 10.9; B.x = –10.9; C.x = 3.3; D.x = –3.3;

Concept B

Example 2A Solve by Subtracting A. Solve 32 = y Check your solution. 32=y + 12Write the equation. 20=yAdditive Inverse and Identity Properties –12=–12Subtraction Property of Equality Answer: The solution is 20.

Example 2A Solve by Subtracting Check32=y + 12Write the equation. ? 32= Check to see if the equation is true. 32= 32The sentence is true.

Example 2B Solve by Subtracting B. Solve x = 4.2. Check your solution. x = 4.2Write the equation. x = –2.7Additive Inverse and Identity Properties –6.9=–6.9Subtraction Property of Equality Answer: The solution is –2.7.

Example 2B Solve by Subtracting Checkx + 6.9=4.2Write the equation. ? – =4.2Check to see if the equation is true. 4.2= 4.2The sentence is true.

Example 2A A.–19 B.–9 C.9 D.19 A. Solve 14 = t + 5.

Example 2B A.–6.3 B.–3.3 C.3.3 D.6.3 B. Solve r = 1.5.

Example 3 Solve by Subtracting MOUNTAINS Driskill Mountain, with a height of 535 feet, is the highest point in Louisiana. It is 8214 feet lower than Guadalupe Peak, which is the highest point in Texas. Write and solve a subtraction equation to find the height of Guadalupe Peak. Let h = the height of Guadalupe Peak. 535= h – 8214Write the equation = h – Add 8214 to each side. 8749=hSimplify. Answer: Guadalupe Peak is 8749 feet high.

Example 3 BUILDINGS Write and solve an equation to find the expected height of the Freedom Tower, which is being built at the World Trade Center site in New York City. The Sears Tower in Chicago is 1450 feet tall, which is 326 feet lower than the expected height of the Freedom Tower. A = h + 326; 1124 feet B. h = 1450 – 326; 1124 feet C = h – 326; 1776 feet D – h = 326; 1776 feet

End of the Lesson