One step equations for 6th grade (positive numbers)

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