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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

3. Solving Equations with Variables on Both Sides

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Exercise 3 Page 19

How do you isolate a variable when it is only on one side of the equation?

See solution.

Practice makes perfect

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

LHS+3x=RHS+3x

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

Add terms

5=5x

.LHS /5.=.RHS /5.

5/5 = 5x/5

Calculate quotient

1=x

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

x = 2x-1

LHS-2x=RHS-2x

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

Subtract terms

- x = - 1

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

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

MultNegNegOnePar

- a(- b)=a* b

x = 1

Subchapter links

Communicate Your Answer p.19

Monitoring Progress p.20-22

Exercises p.23-24