LESSON 1 3 SOLVING MULTISTEP EQUATIONS LEARNING OBJECTIVES

LESSON 1 -3 SOLVING MULTI-STEP EQUATIONS LEARNING OBJECTIVE(S): • I CAN SOLVE MULTI-STEP EQUATIONS BY USING THE DISTRIBUTIVE PROPERTY; COMBINING LIKE TERMS; AND USING INVERSE OPERATIONS. • I CAN CREATE EQUATIONS TO REPRESENT REAL -WORLD SITUATIONS. ESSENTIAL QUESTION: How do I solve Multi-Step Equations?

EX. 1: SOLVING MULTI-STEP EQUATIONS I/WE DO: STEPS: Solve each equation. a. ) 2 y - 3 = 7 c. ) - x + 15 = 12 1. Write the original equation. d. ) -12 = - 3 x - 9 2. Use the Distributive Property to simplify if needed. 3. Combine like terms to simplify if needed. 4. Undo Addition or Subtraction using inverse operations. 5. Undo Multiplication or Division using inverse operations. 6. Check solution (answer) by substituting back into the equation for the variable to see if it makes the equation true.

EX. 1: SOLVING MULTI-STEP EQUATIONS I/WE DO: Solve each equation. STEPS: 1. Write the original equation. 2. Use the Distributive Property to simplify if needed. 3. Combine like terms to simplify if needed. 4. Undo Addition or Subtraction using inverse operations. 5. Undo Multiplication or Division using inverseoperations. 6. Check solution (answer) by substituting back into the equation for the variable to see if it makes the equation true.

EX. 1: SOLVING MULTI-STEP EQUATIONS I/WE DO: STEPS: Solve each equation. h. ) 2 c + c +12= 78 j. ) -2(b - 4) = 12 1. Write the original equation. i. ) 3 a + 6 + a = 90 k. ) 15 = -3(x - 1) + 9 2. Use the Distributive Property to simplify if needed. 3. Combine like terms to simplify if needed. 4. Undo Addition or Subtraction using inverse operations. 5. Undo Multiplication or Division using inverse operations. 6. Check solution (answer) by substituting back into the equation for the variable to see if it makes the equation true.

EX. 1: SOLVING MULTI-STEP EQUATIONS CONTINUED YOU DO: Solve each equation. l. -2 y + 5 y = 14 m. -3 z + 8 + (-2 z) = -12 n. 13 y + 48 = 8 y - 47 o. 3 x-7(2 x -13) = 3 (-2 x + 9) p. m - 5(m - 1) = 7 q. 6(t - 2) = 2(9 – t)

EX. 2: SOLVING A FORMULA FOR ONE OF ITS VARIABLES. I/WE DO: Solve each equation for the indicated variable. STEPS: 1. Isolate the indicated variable using inverse operations. 2. State any restrictions on appropriate variables. Solve for x and state any restrictions on appropriate variables.

EX. 2: SOLVING A FORMULA FOR ONE OF ITS VARIABLES. YOU DO: Solve each equation. STEPS: 1. Isolate the indicated variable using inverse operations. 2. State any restrictions on the variable. Solve for x and state any restrictions on appropriate variables.

EX. 3: REAL – WORLD APPLICATION: I/WE DO: Answer each problem using the steps provided. . a. ) Geometry: The lengths of the sides of a triangle are in the ratio 3: 4: 5. The perimeter of the triangle is 18 in. Find the lengths of the sides. STEPS: 1. Mark the text by doing the following: • Circle all of the numbers. • Underline all of the verbal phrases that go with each number you circled. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 3. Write an equation. 4. Solve the Equation. 5. Answer the question in a complete sentence.

EX. 3: REAL – WORLD APPLICATION: I/WE DO: Answer each problem using the steps provided. . b. ) Aeronautics: Radar detected an unidentified plane 500 miles away, approaching at 700 mi/hr. Fifteen minutes later an interceptor plane was dispatched, traveling at 800 mi/hr. How long did the interceptor take to reach the approaching plane? STEPS: 1. Mark the text by doing the following: • Circle all of the numbers. • Underline all of the verbal phrases that go with each number you circled. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 3. Write an equation. 4. Solve the Equation. 5. Answer the question in a complete sentence.

EX. 3: REAL – WORLD APPLICATION: STEPS: 1. Mark the text by doing the following: I/WE DO: • Circle all of the numbers. Answer each problem using the steps provided. . • Underline all of the verbal c. ) A dog kennel owner has 100 ft. of fencing to enclose phrases that go with each a rectangular dog run. She wants it to be 5 times as number you circled. long as it is wide. Find the dimensions of the dog run. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 3. Write an equation. 4. Solve the Equation. 5. Answer the question in a complete sentence.

EX. 3: REAL – WORLD APPLICATION: I/WE DO: Answer each problem using the steps provided. . d. ) Two buses leave Fresno at the same time and travel in opposite directions. One bus averages 55 mph and the other 45 mph. When will they be 400 miles apart? Note: distance = (rate)(time) or d=rt 400 STEPS: 1. Mark the text by doing the following: • Circle all of the numbers. • Underline all of the verbal phrases that go with each number you circled. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 3. Write an equation. 55 t 4. Solve the Equation. 5. Answer the question in a complete sentence.

EX. 3: REAL – WORLD APPLICATION: I/WE DO: Answer each problem using the steps provided. . e. ) The sum of three consecutive integers is 90. Find the three integers. STEPS: 1. Mark the text by doing the following: • Circle all of the numbers. • Underline all of the verbal phrases that go with each number you circled. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 3. Write an equation. 4. Solve the Equation. 5. Answer the question in a complete sentence.

EX. 3: REAL – WORLD APPLICATION: YOU DO: Answer each problem using the steps provided. . f. ) Mike and Adam left a bus terminal at the same time and traveled in opposite directions. Mike’s bus was in heavy traffic and had to travel 20 mi/h slower than Adam’s bus. After 3 hours, their buses were 270 miles apart. How fast was each bus going? Note: distance = (rate)(time) or d = rt STEPS: 1. Mark the text by doing the following: • Circle all of the numbers. • Underline all of the verbal phrases that go with each number you circled. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 270 3. Write an equation. Mike Adam 4. Solve the Equation. 5. Answer the question in a complete sentence.

EX. 3: REAL – WORLD APPLICATION: STEPS: 1. Mark the text by doing YOU DO: the following: Answer each problem using the steps provided. . • Circle all of the numbers. g. ) The sides of a triangle are in the ratio 5 : 12 : 13. What • Underline all of the verbal is the length of each side of the triangle if the perimeter phrases that go with each of the triangle is 15 in. ? number you circled. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 3. Write an equation. 4. Solve the Equation. 5. Answer the question in a complete sentence.

EX. 3: REAL – WORLD APPLICATION: STEPS: 1. Mark the text by doing YOU DO: the following: Answer each problem using the steps provided. . • Circle all of the numbers. h. ) Adrian will use part of garage wall as one of the long • Underline all of the verbal sides of a rectangular rabbit pen. He wants the pen to phrases that go with each be 3 times as long as it is wide. He plans to use 68 ft. of number you circled. fencing. Find the dimensions of the rabbit pen. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 3. Write an equation. 4. Solve the Equation. 5. Answer the question in a complete sentence.

EX. 3: REAL – WORLD APPLICATION: YOU DO: Answer each problem using the steps provided. . STEPS: 1. Mark the text by doing the following: • Circle all of the numbers. • Underline all of the verbal phrases that go with each number you circled. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 3. Write an equation. 4. Solve the Equation. 5. Answer the question in a complete sentence.

EX. 3: REAL – WORLD APPLICATION: STEPS: 1. Mark the text by doing YOU DO: the following: Answer each problem using the steps provided. . • Circle all of the numbers. j. ) The sum of four consecutive odd integers is 184. Find • Underline all of the verbal the four integers. phrases that go with each number you circled. • Draw a rectangle or box around the question in the problem. 2. Define a variable. 3. Write an equation. 4. Solve the Equation. 5. Answer the question in a complete sentence.