- Topics At a Glance
- Arithmetic, Geometric & Exponential Patterns
- Algebraic Expressions
- Evaluating Algebraic Expressions
- Combining Like Terms
- Distributive Property
- Multiplying Monomials
- Multiplying Binomials
- Dividing Polynomials
- Graphing X-Y Points
- Solving One-Step Equations
- Solving Two-Step Equations
- Solving More Complex Equations
- Solving Equations with Variables on Both Sides
**Solving Funky Equations**- Graphing Inequalities
- Solving Inequalities
- Graphing Lines
- Intercepts
- Graphing Horizontal & Vertical Lines
- Graphing Lines By Plotting Points
- Slope-Intercept Form
- Solving Multiple Equations by Graphing

Sometimes you will solve an equation that has a funky answer, like 10 = 8 or y = y. This doesn't necessarily mean that you did anything wrong, it might very well mean that all *or* no numbers work. Here are some of these equations:

**All Real Numbers Example**

distribute the 3 | |

subtract 24 from each side | |

divide each side by 3 | |

well duh! | |

x = all real numbers |

This means that any number we choose for x will make the equation true. We should verify that this is the correct answer by doing just that, picking a few different numbers and seeing if they work. Let's pick easy numbers like 1 and 2.

See, it all works.

BTW, did you notice that if you had distributed the 3 in 3(x + 8) at the beginning of the problem, the expressions on each side of the equal sign would have been the same?

**No Solution Example**

multiply 2(-3y) | |

add 6y to each side | |

wait, | |

no solution |

This equation does not work. Since 5 ≠ 1, there is no number we can substitute for y to make this equation true.

Unfortunately this one is harder to verify since it would be impossible to check that every number does not work. The best way to make sure the answer is correct is to redo the problem.

Exercise 1

Solve for x: .

Exercise 2

Solve for j: .

Exercise 3

Solve for m: .

Exercise 4

Solve for y: .