# solving linear equations

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1.3: Solving Linear EquationsGoals:

Solve a linear equation for a specified variable

2. Describe the steps necessary to solving linear equations

Review of Terms1) Variable2) Coefficient3) Constant4) Expression5) EquationThroughout Algebra 2, you will hear many different terms being used to describe the parts of an equation or expression.

You will need to know the definition of the following terms throughout the course.

Review of Terms1) Variable2) Coefficient3) Constant4) Expression5) EquationVariable:A letter which is used to represent an unknown number or value.

Any letter can be used as a variable.

Review of Terms1) Variable2) Coefficient3) Constant4) Expression5) EquationCoefficient:The number in front of a variable in a mathematical equation or expression.

The coefficient is actually being multiplied by the variable

Coefficient: 3Means: 3 times xCoefficient: Means: times x2

Review of Terms1) Variable2) Coefficient3) Constant4) Expression5) EquationConstant:A number being added or subtracted from a variable in an equation or expression.The constant in the above expression is: 9

Review of Terms1) Variable2) Coefficient3) Constant4) Expression5) EquationExpression:Contains at least one variable.Examples:

Review of Terms1) Variable2) Coefficient3) Constant4) Expression5) EquationEquation:A sentence that states that two mathematical expressions are equal.Examples:

Steps to Solving Linear EquationsSimplify each side of the equation, if needed, by distributing or combining like terms.

2. Move variables to one side of the equation by using the opposite operation of addition or subtraction.

3. Isolate the variable by applying the opposite operation to each side.a. First, use the opposite operation of addition or subtraction. b. Second, use the opposite operation of multiplication or division.

4. Check your answer.

Simplify: Use the distributive propertySTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Simplify: Combine like termsSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Isolate Variables: Undo the additionSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Isolate Variables: Undo the multiplicationSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Check your answer: Substitute the value of x back inSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

STEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:The answer is true; therefore, the vale of x is true.

Simplify: Use the distributive propertySTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Move Variables: Move the -15x to the other side of the equation.STEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Isolate Variables: Undo the additionSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Isolate Variables: Undo the multiplicationSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Check your answer: Substitute the value of x back inSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

The answer is true; therefore, the vale of x is true.STEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Isolate Variables: Undo the additionSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Isolate Variables: Undo the divisionSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Isolate Variables: Undo the multiplicationSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

Check your answer: Substitute the value of x back inSTEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE:

The answer is true; therefore, the vale of x is true.STEPS TO SOLVING:

1) Simplify

2) Move Variables

3) Isolate Variables a. Undo addition/subtraction b. Undo multiplication/division

4) Check your answerEXAMPLE: