One-Step equations (lesson)

Variables

​Variables are letters in math

Variables represent numbers where the value can change in a linear equation. We try to solve linear equations by getting the variable alone on one side of the equal side.

Linear Equations

Linear equations are mostly found in the form of y=b+mx. Where b is any number that we consider a constant and is considered also the y-intercept. While m is the slope of the linear equation.

Constants & Slope

In the equation y=b+mx, we are told the b is a constant and the y-intercept. While m is the slope. Below is an example where the slope and y-intercept are identified for you. Pay close attention to where the slope, m, is in relation to the x and where the y-intercept, b, is.

y=3-2x slope= -2 y-intercept: (0,3)

Multiple Choice

Where is the constant in this equation

y=3x-17

• 17

• -17

• 3

• 3x

Multiple Choice

What is the slope of this equation

y=3x-17?

• 3

• 3x

• -17

• 3x-17

Inverses

Inverses have to do with oppposites. Solving one step equations requires us to identify inverses of values.
Original Inverse

Addition Subtraction

Subtraction Addition

Division Multiplication

Multiplication Division

Solving one variable equations

While linear equations have both x and y. We want to first start by learning to solve for one variable. This variable can be any letter of the alphabet from a-z. The variable must be equal to a number.

Example: x=15-7 step 1: is there a variable alone on one side of the equal side

x=8 step2: combine by addition, subtraction, division, multiplication

Solving more One step equations

Example 2: b-7=18 step 1: add or subtract any number on the same side as the variable or letter

b-7=18 step 2: Since 7 is on the same side of the equal side we want

+7 +7 to move this value to the other side. First we have to

change the sign. Since its minus 7 we change it to

plus 7.

b=25 this is the solution. We have a letter alone on one side of the equal sign and a number on the other side of that equal sign

Multiple Choice

What is the solution?

j=17+19

• j=33

• 37

• 36

• j=36

Multiple Choice

i=(15-7) $$\times$$ 3

• i=66

• 2

• i=24

• 55

Two or More Variables

When you have two or more of the same variables, make sure you add or subtract the values.

Example: h+h= 3h+17 Step 1: combine any variables of values.

2h=3h+17 Step 2: Move the variables to the same side

-2h -2h

0=h+17 Step 3: get you variable alone

-17 -17

-17 = h