Solving Equations by Adding or Subtracting Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1

Warm Up Evaluate. 1.  + 4 2. 0.51 + (0.29) 1.  + 4 2. 0.51 + (0.29) Give the opposite of each number. 3. 8 4.  Evaluate each expression for a = 3 and b = 2. 5. a + 5 6. 12  b 2 3 1 3 3 2 0.8 2 3 2 3 –8 8 14

Warm Up Evaluate each expression. 1. (–7)(2.8) 2. 0.96 ÷ 6 3. (–9)(–9) 4. 5. 6. 19.6 0.16 81 1 2 3 1.8

Essential Questions How can you solve one-step equations in one variable by using addition or subtraction? How can you solve one-step equations in one variable by using multiplication or division?

Vocabulary equation solution of an equation

An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. To find solutions, isolate the variable. A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side.

Inverse Operations Operation Inverse Operation Isolate a variable by using inverse operations which "undo" operations on the variable. An equation is like a balanced scale. To keep the balance, perform the same operation on both sides. Inverse Operations Operation Inverse Operation Addition Subtraction Subtraction Addition

Example 1B: Solving Equations by Using Addition Solve the equation. Check your answer. = z – 7 16 5 Since is subtracted from z, add to both sides to undo the subtraction. 7 16 + 7 16 = z 3 4 Check = z – 7 16 5 To check your solution, substitute for z in the original equation. 3 4 3 4 5 16 7 – 5 16 

Example 1A: Solving Equations by Using Addition Solve the equation. Check your answer. y – 8 = 24 + 8 + 8 Since 8 is subtracted from y, add 8 to both sides to undo the subtraction. y = 32 Check y – 8 = 24 To check your solution, substitute 32 for y in the original equation. 32 – 8 24 24 24 

Check It Out! Example 4 A person's maximum heart rate is the highest rate, in beats per minute, that the person's heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find a person's age if the person's maximum heart rate is 185 beats per minute.

Check It Out! Example 4 Continued age added to 220 maximum heart rate is a + r = 220 a + r = 220 Write an equation to represent the relationship. a + 185 = 220 Substitute 185 for r. Since 185 is added to a, subtract 185 from both sides to undo the addition. – 185 – 185 a = 35 A person whose maximum heart rate is 185 beats per minute would be 35 years old.

decrease in population Example 4: Application Over 20 years, the population of a town decreased by 275 people to a population of 850. Write and solve an equation to find the original population. original population minus current population decrease in population is p – d = c p – 275 =850 Substitute 275 for d and 850 for c. p – 275 = 850 Since 275 is subtracted from p, add 275 to both sides to undo the subtraction. + 275 + 275 p =1125 The original population was 1125 people.

Inverse Operations Operation Inverse Operation Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable. Inverse Operations Operation Inverse Operation Multiplication Division Division Multiplication

Example 1A: Solving Equations by Using Multiplication Solve the equation. –8 = j 3 Since j is divided by 3, multiply both sides by 3 to undo the division. –24 = j Check –8 = j 3 –8 –24 3 To check your solution, substitute –24 for j in the original equation. –8 –8 

Example 2A: Solving Equations by Using Division Solve the equation. Check your answer. 9y = 108 Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. y = 12 Check 9y = 108 To check your solution, substitute 12 for y in the original equation. 9(12) 108 108 108 

Check It Out! Example 3b Solve the equation. 4j 2 = 6 3 is the same as j. 4 6 4j The reciprocal of is . Since j is multiplied by , multiply both sides by . 4 6 j = 1

Example 4: Application Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year. 1 4 one-fourth times earnings equals college fund Write an equation to represent the relationship. Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. m = $1140 Ciro earned $1140 mowing lawns.

Write an equation to represent the relationship. Check it Out! Example 4 The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began. Distance divided by 3 equals height in thousands of feet Write an equation to represent the relationship. Substitute 45 for d. 15 = h The plane was flying at 15,000 ft when the descent began.

Properties of Equality 3 = 3 3 + 2 = 3 + 2 5 = 5 a = b a + c = b + c WORDS Addition Property of Equality You can add the same number to both sides of an equation, and the statement will still be true. NUMBERS 3 = 3 3 + 2 = 3 + 2 5 = 5 ALGEBRA a = b a + c = b + c

Properties of Equality 7 = 7 7 – 5 = 7 – 5 2 = 2 a = b a – c = b – c WORDS Subtraction Property of Equality You can subtract the same number from both sides of an equation, and the statement will still be true. NUMBERS 7 = 7 7 – 5 = 7 – 5 2 = 2 ALGEBRA a = b a – c = b – c

Lesson Quiz 1. r – 4 = –8 2. –4 3. m + 13 = 58 4. 0.75 = n + 0.6 Solve each equation. 1. r – 4 = –8 2. 3. m + 13 = 58 4. 0.75 = n + 0.6 5. –5 + c = 22 6. This year a high school had 578 sophomores enrolled. This is 89 less than the number enrolled last year. Write and solve an equation to find the number of sophomores enrolled last year. –4 45 0.15 27 s – 89 = 578; s = 667

Lesson Quiz: Part 1 1. 2. 21 3. 8y = 4 4. 126 = 9q 2.8 5. 6. –14 40 Solve each equation. 1. 2. 3. 8y = 4 4. 126 = 9q 5. 6. 21 2.8 –14 40

Lesson Quiz: Part 2 7. A person's weight on Venus is about his or her weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus. 9 10