Solving 1 Step Integer Equations Objective To solve

Solving 1 -Step Integer Equations Objective: To solve one-step integer equations using addition, subtraction, multiplication, and division

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

A one-step equation is as straightforward as it sounds. Solving equations is just a matter of undoing operations that are being done to the variable. By preforming the inverse operation

Solving One-Step Equations • Inverse Operation • Operations that “undo” each other Operation Inverse Operation Addition Subtraction Addition Multiplication Division Multiplication

Solving Equations Using Addition or Subtraction: • If a number has been added to the variable, subtract that number from both sides of the equation. • Also known as balancing the equation

Example 1: Solve m + 7 = 11 - 7 -7 m = 4 Check the solution. Replace the variable with your answer. m + 7 = 11 (4) + 7 = 11 11 = 11

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

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

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.

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

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

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

Practice: Solve and Check • 1. x-(-8)=4 • 3. x/7=-12 2. -5 x=19

Practice: Solve and Check • 4. x+7=-2 5. -4 x=6

Practice: Solve and Check • 6. 9=5+x 7. -5. 1+x=-7. 25