Exercise 3 Page 19

To solve an equation with variables on both sides, you follow almost the same exact rules as solving an equation with variables on one side. The Addition, Subtraction, Multiplication, and Division Properties of Equality will still hold, even for variables. Use these properties and combine like terms, same as always.

Examples

Let's look at a couple examples. Here is one where you would use the Addition and Division Properties of Equality.

-3x+5=2x

AddEqn

LHS+3x=RHS+3x

-3x+5+3x=2x+3x

AddTerms

Add terms

5=5x

DivEqn

.LHS /5.=.RHS /5.

5/5 = 5x/5

CalcQuot

Calculate quotient

1=x

Next we have one exercise where we will use the Subtraction and Multiplication Properties of Equality.

x = 2x-1

SubEqn

LHS-2x=RHS-2x

x-2x=2x-1-2x

SubTerms

Subtract terms

- x = - 1

MultEqn

LHS * (-1)=RHS* (-1)

- x (-1) = - 1 (- 1)

MultNegNegOnePar

- a(- b)=a* b

x = 1