(8) Lesson 2.4 - Solve Equations with Variables on Each Side

30 Nov 2018
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(8) Lesson 2.4 - Solve Equations with Variables on Each Side

• 1. Course 3, Lesson 2-4 Use the work backward strategy to solve Exercises 1-3. 1. Alicia arrived home at 7:45 P.M. from a restaurant. She spent 45 minutes waiting in the restaurant lobby and one and a half hours eating dinner. If it took her 20 minutes to drive home, what time did she arrive at the restaurant? 2. Marcus has \$6 left over after his trip to the movie theater. If his movie ticket cost \$5.50 and he purchased a drink for \$3.00, and a bag of popcorn for \$3.50, and a box of candy for \$2.00, how much money did he originally take to the movie theater? 3. Candace’s quiz scores are 86, 98, 85, 94, and 89. What is the minimum score she can make on her next quiz to maintain a quiz average of at least 90? 4. At nine months of age, a baby elephant can weigh 700 pounds. If this is 4 times the baby elephant’s birth weight, how many pounds did the elephant weigh at birth?
• 2. Course 3, Lesson 2-4 ANSWERS 1. 5:10 P.M. 2. \$20 3. 88 4. 175 pounds
• 3. WHAT is equivalence? Expressions and Equations Course 3, Lesson 2-4
• 4. • 8.EE.7 Solve linear equations in one variable. • 8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). • 8.EE.7b Solve linear equations with rational numbers coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Course 3, Lesson 2-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Expressions and Equations
• 5. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. Course 3, Lesson 2-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Expressions and Equations
• 6. To solve equations with • variables on both sides • rational coefficients Course 3, Lesson 2-4 Expressions and Equations
• 7. 1 Need Another Example? 2 3 4 Step-by-Step Example 1. Solve 8 + 4d = 5d. Check your solution. 8 + 4d = 5d Write the equation. Write the original equation.Check 8 + 4d = 5d 8 = d Subtraction Property of Equality To check your solution, replace d with 8 in the original equation. Simplify by combining like terms. Subtract 4d from the left side of the equation to isolate the variable. Subtract 4d from the right side of the equation to keep it balanced. Replace d with 8. The sentence is true. 8 + 4(8) = 5(8) 40 = 40 ? –4d = – 4d
• 8. Answer Need Another Example? Solve 7x + 4 = 9x. Check your solution. 2
• 9. 1 Need Another Example? 2 3 4 5 Step-by-Step Example 2. Solve 6n – 1 = 4n – 5. 6n – 1 = 4n – 5 Write the equation. Write the original equation.Check 6n – 1 = 4n – 5 Subtraction Property of Equality Simplify. Replace d with 8. The sentence is true. 6(–2) – 1 = 4(–2) – 5 –13 = –13 ? 2n – 1 = –5 Addition Property of Equality Simplify.2n = –4 Mentally divide each side by 2.n = –2 – 4n = – 4n + 1 = + 1
• 10. Answer Need Another Example? Solve 3x – 2 = 8x + 13. Check your solution. –3
• 11. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 3. Green’s Gym charges a one time fee of \$50 plus \$30 per session for a personal trainer. A new fitness center charges a yearly fee of \$250 plus \$10 for each session with a trainer. For how many sessions is the cost of the two plans the same? 20s = 200 Simplify. Check Green’s Gym: \$50 plus 10 sessions at \$30 per session Simplify. Addition Property of Equality 50 + 10 • 30 = 50 + 300 250 + 10 • 10 = 250 + 100 50 + 20s = 250 Subtraction Property of Equality Write the equation.50 + 30s = 250 + 10s fee of \$50 plus \$30 per session Words Let s represent the number of sessions.Variable 50 + 30s = 250 + 10sEquation is the same as a fee of \$250 plus \$10 per session Division Property of Equality s = 10 So, the cost is the same for 10 personal trainer sessions. Simplify. = \$350 new fitness center: \$250 plus 10 sessions at \$10 per session = \$350 – 10s = – 10s – 50 = – 50
• 12. Answer Need Another Example? The measure of an angle is 8 degrees more than its complement. If x represents the measure of the angle and 90 – x represents the measure of its complement, what is the measure of the angle? 49°
• 13. 1 Need Another Example? 2 3 4 Step-by-Step Example 4. Solve x – 1 = 9 – x. x = 12 Simplify. Multiplicative Inverse Property Addition Property of Equality The common denominator of the coefficients is 6. Rewrite the equation. Addition Property of Equality Simplify. Simplify. + 1 = + 1
• 14. Answer Need Another Example? Solve x + 2 = 7 + x. 12
• 15. How did what you learned today help you answer the WHAT is equivalence? Course 3, Lesson 2-4 Expressions and Equations
• 16. How did what you learned today help you answer the WHAT is equivalence? Course 3, Lesson 2-4 Expressions and Equations Sample answers: • When variables are on both sides of the equation, use the properties of equality to write an equivalent equation with the variables on one side. • You can check the solution to an equation by replacing the variable with the solution in the original equation.
• 17. Name the procedures you would use to solve an equation with variable terms on both sides such as 3x + 5 = 6x + 2. Course 3, Lesson 2-4 Ratios and Proportional RelationshipsExpressions and Equations