Equations Variable on Both Sides

Equations Variable on Both Sides

Expression Review

Expressions are made up of terms.

Terms are variables, constants, or variables with coefficients. Terms are separated with plus(+) or minus(-) symbols.

Variable:Letter of symbol

Coefficients: in front of variable

Constant: a number by itself

Equations

An equation is when two expressions are equal.

5x+1 is an expression

3x+5 is an expression

The image shows that the two expressions are equal.

5x+1=3x+5 is an equation.

Multiple Select

5x + 1 = 3x + 5

Select the expressions from the choices below.

• 3

• 3x

• 3x+5

• 5

• 5x+1

Variable to one side

Our goal is to get one variable (letter or symbol) on one side and one constant (lonely number) on the other side.

Variable(x) = constant(number)

First we remove the variables from one side, but we must do this to both sides to keep the equation balanced.

Multiple Choice

5x + 1 = 3x + 5

If we subtract 3x from both sides what do we get?

• 5x-2=3x-2

• 2x + 1 = 5

• 6x = 8x

Variables on one side

When we subtract 3x,

the left side has 2x left and

the right side has no x.

Now x is only on one side.

Next we need to get the constants on one side.

Two Step Equation

Now that we have a variable and a constant on one side and only a constant on the other side, you might notice we have a two step equation.

To solve the two step equation we need to get the variable alone by itself.

2x + 1 = 5

Multiple Choice

The first thing we need to do to get the variable by itself is

2x + 1 = 5

• Divide by 2

• Subtract 5

• Divide by 5

• Subtract 1

One Step Equation

2x + 1 = 5

After we subtract one from each side we have a one step equation.

All variables are on one side and constants are on the other

All we need to do now is isolate the variable.

2x = 4

Divide both sides by 2 and get

x = 4

Multiple Choice

2x + 5 = 3x -2

If I subtract 2x from the right side what equation would I get?

• 5=x-2

• 2x+3=3x

• 5=3x-2

• 2x+5=-2