This document discusses how to solve one-step integer equations using addition, subtraction, multiplication, and division. It explains that the inverse operations can be used to undo operations on both sides of the equation. Examples are provided to show solving equations by adding or subtracting to undo additions or subtractions, and dividing or multiplying to undo multiplications or divisions. Practice problems are included for the reader to try.

1. SOLVING 1-STEP INTEGER EQUATIONS Objective: To solve one-step integer equations using addition, subtraction, multiplication, and division

2. Solve an Equation To find all values of a variable that make an equation true

3. A one-step equation is as straightforward as it sounds. You will only need to perform one step in order to solve the equation.

4. Solving One-Step Equations Inverse Operation Operations that “undo” each other For example, addition “undoes” subtraction and subtraction “undoes” addition. Multiplication is the inverse of division

5. Solving Equations Using Addition or Subtraction : If a number has been added to the variable, subtract that number from both sides of the equation. If a number has been subtracted from the variable, add that number to both sides of the equation.

6. Example 1: Solve m + 7 = 11 m + 7 = 11 To undo the addition of 7, subtract 7 from both sides of the equal sign. - 7 -7 m = 4 Check the solution. m + 7 = 11 Replace the variable with your answer. (4) + 7 = 11 11 = 11 

7. Example 2: Solve -6 = m - 4 -6 = m - 4 To undo the subtraction of 4, add 4 to both sides of the equal sign. +4 +4 -2 = m Check the solution. -6 = m - 4 Replace the variable with your answer. -6 = (-2) - 4 -6 = -6 

8. Practice j - 3 = -12 -4 + r = 26 +3 +3 j = - 9 +4 +4 r = 30

9. Solving Equations Using Multiplication or Division If a variable has been multiplied by a nonzero number, divide both sides by that number. If a variable has been divided by a number, multiply both sides by that number.

10. 3 y = 261 To undo the multiplication by 3, divide 3 from both sides of the equal sign. 3 3 y = 87 Check the solution. 3 y = 261 Replace the variable with your answer. 3(87) = 261 261 = 261  Example 3: Solve 3y = 261

11. - 1 w = 42 To undo the multiplication of -1 , divide both sides by -1. -1 -1 w = -42 Check the solution. -w = 42 Replace the variable with your answer. - (-42) = 42 42 = 42  Example 4: Use the multiplication property of - 1 - w = 42 -1 is being multiplied to w

12. Practice -6 x = -36 b = 12 -6 -6 x = 6 (-4) -4 (-4) b = -48