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SOLVING 1-STEP SOLVING 1-STEP INTEGER INTEGER
EQUATIONSEQUATIONSObjective: Objective: To solve one-step integer
equations using addition, subtraction, multiplication, and
division
Solve an EquationSolve 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 Solving Equations Using Addition or SubtractionSubtraction::
• 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: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 = 11Replace the variable
with your answer.
(4) + 7 = 11 11 = 11
Example 2: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 - 4Replace the variable
with your answer.
-6 = (-2) - 4 -6 = -6
Practice j - 3 = -12 -4 + r = 26 +3 +3
j = - 9 +4 +4
r = 30
Solving Equations Using Solving Equations Using Multiplication or DivisionMultiplication 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.
3y = 261To undo the
multiplication by 3, divide 3 from both sides of the equal
sign.
3 3 y = 87
Check the solution.
3y = 261Replace the variable
with your answer.
3(87) = 261 261 = 261
Example 3:Example 3: Solve 3y = 261
-1w = 42To undo the
multiplication of -1 , divide both
sides by -1.-1 -1 w = -42
Check the solution.-w = 42Replace the
variable with your answer.
-(-42) = 42 42 = 42
Example 4:Example 4:Use the multiplication property of - 1
-w = 42-1 is being multiplied
to w
Practice -6x = -36 b = 12 -6 -6
x = 6
(-4)-4
(-4)
b = -48