Lesson 2: 2-2 Solving one-step equations

What is the problem asking you to find?

What is another way to solve the problem?

How can you check that your solution is correct?

solve an equation
equivalent equation
linear equation

A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

3A Functions
3B Functions
3C Functions

Solving an equation means finding the value of the variable in the equation that makes the equation true. To solve an equation, isolate the variable (with a coefficient of 1) on one side of the equation. Use the Properties of Equality to maintain equivalent equations in each step of the process.

The Daytona 500 is widely considered to be the most important event of the NASCAR circuit. The distance around the track is 2.5 miles, and the race is a total of 500 miles. How many laps does it take to finish the race?

Ricardo is driving 780 miles to Memphis. He drove about 3/5 of the distance on the first day. About how many miles did Ricardo drive?

Coefficients: Students are sometimes confused about what to do with a variable in an equation such as –x = 27. Point out that the variable actually has a coefficient of –1. Remembering that the product of two negative numbers is a positive, you can multiply each side of the equation by –1.

Isolating Variables Explain that when isolating a variable, it does not matter whether the variable ends up on the left or right side of an equation. For example, the solution of 8 = 15 + z is still –7, even though the final step may be –7 = z.

Preventing Errors: Students may try to skip a step and solve the problem without first writing the equation. Tell students that they will make fewer mistakes in solving equations if they translate the sentence and write the equation before solving it.

If some students are having trouble solving equations by addition or subtraction, then write x and two numbers on the board. Give students the operation symbols + and -. Tell them to use both of the numbers, x, and the operation symbols to write two equations for which the value of x is the same. Have students solve for x in both equations. For example, suppose the two numbers were 23 and 45. Students could write x + 23 = 45 and x = 45 - 23. For both equations the solution is 22.

Write an equation involving multiplication or division on the board. Have students identify the operation in the equation. Based on the operation they identify, have students suggest the operation that might be used to solve the equation.

Exercises 1 - 17

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