onestepequations

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