Algebra: Chapter 3-3 and 3-4, pages 125 and 130
Using the Properties Together
You can solve these equations in a variety of ways. Remember the objective is to ISOLATE the variable on one side. You can add, subtract, multiply or divide the same thing on both sides of the equation.
Follow these 4 steps:
- you should solve equations with parenthesis using the distributive property
- if there are like terms on one side of the equation, collect those first.
- add and subtract the constants
- finally, multiply or divide by the coefficient (next to the variable) to isolate the variable
Practice makes perfect and be sure to SHOW ALL THE STEPS! Purplemath has some examples here about these multi-step equations.
Don’t forget to use the reciprocal, its sometimes the same as dividing but faster.
DO NOT TAKE ANY SHORTCUTS, SHOW ALL THE WORK IN ALL ITS GORY DETAIL, THIS WILL REALLY SAVE YOU IN THE LONG RUN BY CUTTING DOWN ON SILLY MISTAKES!!
Expressions and Equations
The phrase the quantity suggests a grouping of terms will follow. The words sum of, difference of , product of and quotient of also suggests a grouping of terms (USING PARENTHESES) to follow.
The quantity “3 less than a number” is written `n−3`. The text “4 times the quantity 3 greater than a number” is translated to `4(n+3)`.
Finally, here are some problem-solving guidelines:
Phase 1: UNDERSTAND THE PROBLEM
- What am I trying to find?
- What data am I given?
- Have I ever solved a similar problem?
Phase 2: Develop and carry out a PLAN
- What strategies might I use to solve the problem?
- How can I correctly carry out the strategies I select?
Phase 3: Find the ANSWER and CHECK
- Does the proposed solution check?
- What is the answer to the problem?
- Does the answer seem reasonable?
- Have I stated the answer clearly?