Algebra 2.3 More On Solving Equations

Front 1

Steps for solving a linear equation:

Back 1

1. Simplify each side separately. Clear ( ) using distributive property. Combine like terms.

2. Isolate the varible term on one side. Use the addition, subtraction, multiplication or division proerty of equality so that the variable term is on one side of the equation an a number is on the other.

3. Check. Subsitute the proposed solution into the original equation to see if a true statement results.

Front 2

Steps to solve equations with fractions or decimals as coefficients:

Back 2

Use the "fraction Buster Method"

1. Look art all fractors from both sides, ask what is the overall LCD.

2. Multiply both sides of equation by the LCD, the effect is that it cancells all the denominators.

3. Cancell all denom's with LCd and continue to solve equation.

Front 3

Conditional Equation

Back 3

An equation with exactly one solution { a number }

Front 4

Identity Equation

Back 4

An equation with both sides exactly the same, like 0 = 0. An Identity is true for all replacements of the variable. the solution is always

{all real numbers}

eg. 5x - 15 = 5(x - 3)
5x - 15 = 5x - 15
+15 +15
0 = 0

Front 5

Contradiction Equation

Back 5

The variable disappears, but this time the stmt is false. When this happens the equation has no solution, and is called a contradiction. Its solution set is an empty set, or null set. symbolized by O with a / through it.