Solving Linear Equations

Define and use: Linear Equation in one variable,

Solution types,

Equivalent Equations

Linear Equations

You can use a variable (unknown value) to represent a quantity.

A solution is a set of values that make an equation true.

To solve an equation that has more than one operation, use the properties of equality to isolate the variable.

Use the properties of equality to solve the equation. (Let a, b, c = real numbers.)

Addition Property of Equality

Multiplication Property of Equality

If a=b, then a+c = b+c

If a=b, then ac = bc

Subtraction Property of Equality

Division Property of Equality

If a=b, then a-c = b-c If a=b, then a/c = b/c (c

Solve a Multi-Step Equation.

Solve 4(x-3) = -56. Show each step, and check the answer.

4(x-3) = -56 Given 4x –12 = -56 Distributive Property

4x-12+12 = -56 + 12 Addition Property = Division Property

x = -11 Simplify.

To Check your answer, substitute the solution into the equation

4(x-3) = -56 Given4(-11-3) = -56 Substitution4(-14) = -56 Simplify.-56 = -56 Verify.

Think and Discuss with your elbow partner.

1. What property is used to solve the equation x+3 = 9 ?

2. What property is used to solve the equation 12y = 36?

3. Explain how to solve the equation 4z-5 = 23.