# Solution of Linear Equations. Including Absolute Value Ones.

### There you are in front of a linear equation. You don't know if you need to add both sides or subtract both sides. Do I need to multiply one side or both? May I apply the commutative property to three variables multiplying each other? Learn the properties of equality and apply them in an increasing level of difficulty to the solution of one variable linear equations. Apply them to the solution of absolute value equations. You will have plenty opportunities to see many examples. You will have the option to view a few ones and then you might try to solve the following; if you get stuck, then you just view the solution right after you attempted on your own! Additionally, you may highlight parts of the solution or write notes using the MARKER TOOL menu on the top of the screen. Down the box where the lesson is displayed you have some useful definitions you might try to study first.

Lesson's Content

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Lesson's Glossary

Absolute value:  Distance of a number from zero on a number line. The distance is taken as positive all the time.
For a variable:
If x < 0 then –a; if x>=0 then a.

Equation: A mathematical statement that has to expressions joined by the = sign. It has the right side of the equation (expression1) and the left side of the equation (expression 2)

Equivalent equations: An equation that when solved have the same solution set over a given domain.

Equivalent expressions:  All expressions that represent the same number for any value of the variable that they contain.

Linear equation:  Any equation with all exponents = 1 regardless of the form the equation is represented.

Sides of an equation:  The two expressions at both sides of the equal sign in an equation. Left and right.

Sides of an inequality: The two expressions at both sides of the inequality sign in an inequality. Left and right.

Solve an equation:  To find the solution, to find the answer, to get to know the value for which a variable stands for.

Term: A form of grouping one or more numerical and/or variable factors by means of multiplication and division.

Variable: A letter used to represent a number. When the variable is part of an equation, it is possible to find the value for which it stands for by solving the equation. This is the solution (s) of the equation.

Variable expression: Any expression containing one or more variables.

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