Post on 14-Apr-2017
One-Step Equations VocabularyEquation – a mathematical sentence that contains an equal sign. The equation acts like a balance scale.
Solution – a number that can replace a variable in an equation and make a true statement.
Algebra- A branch of mathematics that includes the use of variables.
Since an equation is like a balance scale, if you do something to one side, then you have to
do it to the other side.
We solve one-step equations by performing the opposite operationor “inverse operation.”
Addition SubtractionSubtractio
nMultiplicationDivision
AdditionDivisionMultiplication
Inverse operations- two operations that have the opposite effect
Addition Subtraction
Multiplication Division
Let’s look at it using algebra
x + 10 = 15
Step 1: Complete
the inverse operation to both sides
of the equation.
- 10 - 10
Step 2: Write or “bring
down” the result.
x = 5
Step 3:Check the solution by “substituting” or “plugging it in”
SolvingOne-StepAddition
Equations
What if the equation were
written this way?
x + 1 = 7
Which operation should we choose
to solve?
x + 1 = 7Subtraction
To keep the equation balanced…..
….we must perform the same operation to both sides.
Since this is addition,we subtract the same number
from both sides.
X + 1 = 7 -1 -1
X + 1 = 7 -1 -1X
= 6
Example 1
m + 18 = 34 Look for variable
-18 -18 Do the inverse
m = 16 Write what m is
m + 18 = 3416 + 18 = 34 substitute in m
34 = 34 Solution is correct!
Example 1 (bar model)
m + 18 = 34 Look for variable Do the inverse
What number does m represent?
m = 16Substitute in m
16 + 18 = 34 34 = 34
Solution is correct!
m 18
34
16 18
34
Solving One-Step
Subtraction Equations
What if the equation were written this
way?
x – 1 = 8
Which operation should we choose
to solve?
x – 1 = 8Addition
To keep the equation balanced…..
….we must perform the same operation to both sides.
Since this is subtraction,we add the same number to both
sides.
x – 1 = 8 + 1 +1
x – 1 = 8 + 1 +1X = 9
Try These...1. r + 5 = 182. m - 26 = 593. 102 = x - 154. a + 39 = 56
r = 13m = 85117 = x a = 17
Solving One-Step
Multiplication Equations
What if the equation were written this
way?
2x = 12
Which operation should we choose
to solve?
2x = 12Division
To keep the equation balanced…..
….we must perform the same operation to both sides.
Since this is multiplication,we divide both sides by the same
number.
2x = 12 2 2
2x = 12 2 2
X
= 6
SolvingOne-Step
Division Equations
What if the equation were written this
way?
x - 2 = 4
Which operation should we choose to
solve?
x - 2 = 4Multiplication
To keep the equation balanced…..
….we must perform the same operation to both sides.
Since this is division,we multiply both sides by
the same number.
x – 2 = 4 2(x – 2) = 2(4)
x – 2 = 42(x – 2) = 2(4)
X
= 8
A check only takes 3 steps:
1. Write the original equation. 2x = 122. Substitute the answer
for the variable. 2(6) = 123. Verify that both sides
are equal. 12 = 12
Your Turn: Practice Worksheets 1- 4