Module 3, Topic 1 Notes

Solving One-Step Linear Equations

To solve linear equations, we use INVERSE OPERATIONS!!!!

• If you see ADDITION, get rid of it by using SUBTRACTION.

• If you see SUBTRACTION, get rid of it by using ADDITION.

• If you see MULTIPLICATION, get rid of it by using DIVISION.

• If you see DIVISION, get rid of it by using MULTIPLICATION.

Here are some examples of One-Step Linear Equations:

1. Solve: x + 12 = -3 - 12 -12

x = -152. Solve: q – 7 = -4 +7 +7 q = 3

3. Solve: 7p = -28 7 7 p = -44. Solve:

y = 40

Remember that you can check your answers by substituting for the missing

variable!1. x + 12 = -3 -15 + 12 = -3 Correct!2. q – 7 = -4 3 – 7 = -4 Correct!3. 7p = -28 7(-4) = -28 Correct!4.

40/4 = 10 Correct!

You may have to write your own equation and then solve it…

• Renaldo needs to buy some folders that are $0.60 each. How many can he buy with $6?

Let x represent the number of folders:

0.60x = 60.60 0.60x = 10Renaldo can buy 10 folders.

• Carmen gave a sales clerk $50 to pay for her $32.75 worth of clothes. How much change should she get?

Let x represent her change.50 – 32.75 = x17.25 = xCarmen should get back

$17.25.

More Examples • If the perimeter of a square

is 240 feet, find the length of one side.

All the sides of a square are of equal length, and we find perimeter by adding up all its sides.

Let x = one side length.4x = 240 4 4x = 60Each side measures 60 feet.

• Write an equation to represent the following statement. Then, solve for the missing number. “Eighty increased by a number is negative twenty.”

Let x be the missing number. 80 + x = -20 -80 -80 x = -100The number is -100.

Some Extra Practice for You!

• Click on the link below to see a few more examples of solving one-step equations. Then, take the 5 question quiz at the end:

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_OneVariableOneStep.xml• Try solving one-step equations AND playing

basketball at the same time with this game:http://www.math-play.com/One-Step-Equation-Game.html