unit 6.4 - solving inequalities by adding and subtracting
what do we need to know
- Know the fundamental difference between equations and inequalities:
An inequality has more a range of possible answers, whereas an equation has only one solution.
- Be able to solve equations by adding and subtracting.
- To solve inequalities by adding and subtracting, we proceed as we would when solving equations by adding and subtracting.
More Information
1. solving inequalities by adding and subtracting
If you know how to solve equations by adding and subtracting, then you know how to solve inequalities by adding and subtracting... You do exactly the same thing! That is, the procedure is the same!!!
Take a look at the following example of solving an EQUATION using adding and subtracting:
The following examples also illustrate the similarity of solving procedure between an equation and an inequality (when adding and subtracting):
More examples of the use of addition and subtraction to solve inequalities:
2. solving inequalities with the variable on both sides of the inequality
sign
look at the following example of inequalities with a variable in both sides of the sign:
1, Decide the side in which the variable is going to stay.
To make things easier, always choose the side in which, after adding and subtracting,
the variable ends up positive, and with a
coefficient of 1 (that is, by itself).
2. Eliminate by adding and subtracting so that you achieve the ghoal listed in 1 above.
3. SOLVING INEQUALITIES THAT involve the distributive property
1. Apply the ORDER OF OPERATIONS (BEDMAS):
- Look "inside" the brackets which make up the distributive property. part of the inequality. Is there anything to solve? If so, solve inside the brackets first.
- According to the ORDER OF OPERATION, we now focus on MULTIPLICATION. That is,
multiplying the digit outside the brackets by each of the terms inside the brackets.THINK ABOUT IT THIS WAY:
A DISTRIBUTIVE PROPERTY is a
NOTHING can be done UNLESS the inequality is unlocked.
THUS, before you do anything else:YOU MUST UNLOCK THE INEQUALITY BY,
yes,
DISTRIBUTING first.
videos that can help
Inequalities using Addition and Subtraction - Video 2
one step inequality involving addition - video 3
interactive online activities
WORKSHEETS
NOTE: Even though I mentioned solving inequalities with variables on both sides of the inequality sign, AND solving inequalities with the distributive propertry, I am going to wait until next part of the UNIT to give you worksheets on these topics.
This worksheets focus solely on solving inequalities using addition and subtraction:
solving_inequalities_-_addition_and_subtraction_1.pdf Download File | solving_inequalities_-_addition_and_subtraction_2.pdf Download File |
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solving_inequalities_-_addition_and_subtraction_3.pdf Download File
| solving_inequalities_-_addition_and_subtraction_4.pdf Download File
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solving_inequalities_-_addition_and_subtraction_5.pdf Download File
| solving_inequalities_-_addition_and_subtraction_6.pdf Download File
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REVIEW - WORKBOOK
Remember the following information when graphing inequalities: