Algebra 1 Section 2.5

Solving Two-Step Equations The operations done to a variable must be undone using inverse operations in reverse order.

Example 1 Solve 2x + 6 = 21. 2x + 6 = 21 2x + 6 – 6 = 21 – 6 2x = 15

Example 1 2x = 15 2x2x 2 = x = Did you check your answer?

Example 2 Solve – 3.6 = a 1.5 – = a 1.5 = -0.8 a 1.5

Example 2 a = -1.2 – 3.6 = -0.8 – 3.6 = = -0.8 a = 1.5(-0.8) a 1.5 ( )

Solving Equations of the Form ax + b = c 1.Undo the addition or subtraction of the constant term. 2.Undo the multiplication or division done to the variable.

Example 3 Solve – 7 = 2. x 3 – = x 3 = 9 x 3

Example 3 x = 27 = 9 x 3 x 3 ( ) 3 = 3(9)

Solving Word Problems Step 1: Read the Problem Draw a picture, if possible Assign a variable to the main unknown

Solving Word Problems Step 2: Plan a Method of Attack Make a table, if possible Translate word phrases into expressions using the variable

Solving Word Problems Step 3: Solve an Equation Write an equation Solve the equation

Solving Word Problems Step 4: Check your Solution Have I answered all of the questions in the problem? What do the numbers represent? Are the answers reasonable?

Example 4 Ninety-seven is twenty-four less than four times a number. 97 – 24=4x4x

Example 5 How many quarters must be removed from $2.64 to leave a total of $1.89? q = number of quarters 0.25q = value of the quarters 2.64 – 0.25q = 1.89

Example 6 The grain elevator weighed Mr. Young’s truck at 17,760 lb before he dumped his wheat. The weight of the empty truck is 6180 lb. If the wheat weighed 60 lb/bu, how many bushels of wheat did he deliver to the elevator?

Example 6 The grain elevator weighed Mr. Young’s truck at 17,760 lb before he dumped his wheat. The weight of the empty truck is 6180 lb. If the wheat weighed 60 lb/bu, how many bushels of wheat did he deliver to the elevator? b = bushels of wheat 60b = the weight of the wheat

Example 6 The grain elevator weighed Mr. Young’s truck at 17,760 lb before he dumped his wheat. The weight of the empty truck is 6180 lb. If the wheat weighed 60 lb/bu, how many bushels of wheat did he deliver to the elevator? 60b = 17,760

Homework: pp