Solving linear equations  Review the properties of equality  Equations that involve simplification  Equations containing fractions  A general strategy for solving linear equations

Solving linear equations  Review the properties of equality  Equations that involve simplification  Equations containing fractions  A general strategy for solving linear equations

The properties of equality The reflexive property of equality a = a The symmetric property of equality a = b if and only if b = a The transitive property of equality If a = b and b = c, then a = c.

The properties of equality The addition property of equality If a = b, then a + c = b + c The multiplication property of equality a = b if and only if ac = bc and c ≠ 0 The same real number, or algebraic expression, may be added to both sides of an equation without changing the solution. Both sides of an equation may be multiplied by the same nonzero real number without changing the solution.

The properties of equality The addition property of equality If a = b, then a + c = b + c The multiplication property of equality If a = b, then ac = bc (c ≠ 0)

When you are asked to solve an equation, you always need to check your proposed solution in the original equation and write your answer in a complete English sentence.

If an equation contains one or more fractions, then the solution process is usually less taxing if you first eliminate the fractions from the equation.

1.Determine the least common multiple of all of the denominators that occur in the equation. 2.Multiply both sides of the equation by the least common multiple found in step 1.

3.Simplify both sides of the equation. Remember to use the distributive property on sides of the equation that contain two or more terms. 4.If you chose the correct LCD and made no mistakes, then the fractions have now been eliminated from the equation.

5.Go ahead and solve this equivalent equation which contains no fractions.

Equations in which the first step would require fraction arithmetic if we didn’t clear the fractions first.

1.Clear fractions by multiplying each side of the equation by the LCM of all of the denominators 2.Simplify each side of the equation 3.Collect all variable terms on one side of the equation and all constant terms on the other side of the equation

4.Isolate the variable and solve. 5.Check the proposed solution in the original equation. 6.State your conclusion in a complete English sentence.