1. § 1.4 Solving Linear Equations

2. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear equation in one variable x is an equation that can be written in the form ax + b = 0, where a and b are real numbers and a is not equal to 0. An example of a linear equation in x is 4x + 2 = 6. Linear equations in x are first degree equations in the variable x.

3. Blitzer, Algebra for College Students, 6e – Slide #3 Section 1.4 Properties of Equality PropertyDefinition Addition Property of Equality The same real number or algebraic expression may be added to both sides of an equation without changing the equation’s solution set. Multiplication Property of Equality The same nonzero real number may multiply both sides of an equation without changing the equation’s solution set.

4. Blitzer, Algebra for College Students, 6e – Slide #4 Section 1.4 Solving Linear Equations Solving a Linear Equation 1) Simplify the algebraic expressions on each side. 2) Collect all the variable terms on one side and all the numbers, or constant terms, on the other side 3) Isolate the variable and solve. 4) Check the proposed solution in the original equation.

5. Blitzer, Algebra for College Students, 6e – Slide #5 Section 1.4 Solving Linear EquationsEXAMPLE SOLUTION Solve 4x + 2 = 10.

6. Blitzer, Algebra for College Students, 6e – Slide #6 Section 1.4 Solving Linear EquationsEXAMPLE SOLUTION Solve 6x -7 = 3x + 8.

7. Blitzer, Algebra for College Students, 6e – Slide #7 Section 1.4 Solving Linear EquationsEXAMPLE SOLUTION Solve: 5 - 3x + 4x = 1 - 7x + 12.

8. Blitzer, Algebra for College Students, 6e – Slide #8 Section 1.4 Categorizing an Equations Type of EquationsDefinitions IdentityAn equation that is true for all real numbers ConditionalAn equation that is not an identity but is true for at least one real number Inconsistent (contradiction) An equation that is not true for any real number

9. Blitzer, Algebra for College Students, 6e – Slide #9 Section 1.4 Categorizing an EquationEXAMPLE SOLUTION Solve and determine whether the equation is an identity, a conditional equation or an inconsistent equation. 5 + 4x = 9x + 5

10. Blitzer, Algebra for College Students, 6e – Slide #10 Section 1.4 Categorizing an EquationEXAMPLE SOLUTION Solve and determine whether the equation is an identity, a conditional equation or an inconsistent equation. 5 – (2x – 4) = 2(x +1) - 4x