Algebra
Lesson 6-3
Vocabulary: NONE
Examples:
EXAMPLE 1- Inequality Involving a Negative Coefficient
-7b+19<-16 Original inequality
-7b+19<-16 Subtract 19 from each side
-19 -19
-7b<-35 Divide each side by -7
-7b< -35
-7 -7
b<5 since you divided by a negative number you need to change the sign from < to >
So b>5 is your answer
Example 2:
Right an inequality for the sentence below, then solve the inequality.
Two times a number minus seventeen is at least four times the number plus twenty.
Two times a number minus seventeen is at least four times the number plus twenty.
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2n - 17 > 4n + 20
Now that we have the equation, we can solve it.
2n - 17 > 4n + 20
2n - 17 - 4n > 4n + 20 - 4n Subtract 4n on each side (you may also subtract 2n, but that may be harder) Combine like terms.
-2n - 17 + 17 > 20 + 17 You have to combine like terms, but you have to keep at least one number on each side, so add 17 to 20.
-2n < 37 Divide each side by -2 to get variable alone, and since you divide by a negative, you flip
-2 -2 the symbol from > to <
Your answer is {n|n < -18.5} or n < -18.5
Example three:
Solving real world problems.
Find the temp. in Celsius for which chlorine is gas
9/5C + 32 > -31 This is the original inequality
9/5C + 32 - 32 > - 31 -32 Subtract 32 from each side
9/5C > - 63 Simplify
(5/9)5/9C > -63(5/9) Multiply 5/9 on each side
C > - 35 Your answer should be that.
Additional Information: Remember that when working with inequalities, don't forget to change the sign whenever you multiply or divide by a negative number.
Always keep at least one number on each side.
Always get the variable alone once you've done the rest.
Pictures:
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