- Find your new seat. Use the chart on the north wall, and make sure the number on your chair matches your number on the chart.
- In your team, explain how to graph -6+-12 on a number line.
- In your team, discuss why
(-6)(-8)=(-1)(-1)(6)(8). - In your team, discuss how to simplify
3(x+6)-(4x+18).
What You Ought to Know about Inequalities:
- Solving inequalities is the same as solving equations unless the coefficient is negative, in which case the inequality symbol needs to be reversed.
- Properties of operations, including their inverses, can be used to isolate and define independent variables.
*"Inverse" means the same as "reverse," so the inverse of multiplication is division, the inverse of subtraction is addition, etc. - Coefficients show multiples of an independent variable.
- Constants show invariable numbers: they do not change because they are not variable, and they are not related to variables.
*"Variable" means it can change. - Independent variables are usually unknown or changeable values.
- Dependent variables are defined by operations with constants, coefficients, and independent variables.
- An open dot like this
is used to graph inequalities that are greater than, >, or less than, <. It means the independent variable is not included in the answer. - A closed dot like this
is used to graph inequalities that are greater than or equal to, ≥, or less than or equal to, ≤. It means the independent variable is included in the answer.
What You've Got to Do
- Extract inequalities from story problems and model with manipulatives.
- Use manipulatives and mathematical writing to show how to solve inequalities.
- Write equations and inequalities to represent real-world variable situations.
- Solve equations and solve and graph inequalities that represent real-world variable situations.
