Bell Ringer SOLVING 1 STEP EQUATIONS WITH RATIONAL

Bell Ringer

SOLVING 1 -STEP EQUATIONS WITH RATIONAL COEFFICIENTS 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. You will only need to perform one step in order to solve the equation.

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

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.

Example 1: Solve m + 7 = 11 - 7 -7 m = 4 To undo the addition of 7, subtract 7 from both sides of the equal sign. 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: Solve 3 y = 261 3 3 y = 87 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 -1 is being multiplied to w -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