Transcript of Math Journal 10-16. Math Journal 10-15 Unit 3 Day 7: Solving Inequalities with Variables on Both...
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- Math Journal 10-16
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- Math Journal 10-15
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- Unit 3 Day 7: Solving Inequalities with Variables on Both Sides
Essential Questions: How do we solve inequalities with variables on
both sides? When does an inequality have no solution or a solution
of all real numbers?
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- Vocabulary No solution: when the variable in an equation or
inequality is eliminated and you are left with a false statement
All real numbers: when the variable in an equation or inequality is
eliminated and you are left with a true statement
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- Example 1: Solve the inequalities. 7x + 19 > -2x + 556x + 22
< -3x + 31 + 2x 9x+ 19> 55 - 19 9x> 36 9 9 x> 4 + 3x
9x+ 22< 31 - 22 9x < 9 9 9 x< 1
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- Example 2: Solve the inequalities. x + 2 > 3x + 1-8x + 7
< 4x 5 - 3x -2x + 2> 1 - 2 -2x> -1 -2 - 4x -12x + 7< -
5 - 7 -12x< -12 -12 x < 2 1 x > 1 -12
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- Example 3: Solve the inequality. (-12x + 16) < 10 3(-x 2) +
4-3x < 10 -3x+ 4 < 16 - 3x -6x + 4< 16 + 3x - 4 -6x< 12
+ 6 + 3x -6 x > -2 4 1 -6
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- Example 4: Solve the inequality. (12x 4) < 2(7 5x) - 26x<
14 + 10x 16x- 2< 14 - 10x + 2 + 10x 16 x < 1 16x< 16 2 1
16
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- Example 5: Solve the inequalities. 12 2a 3 x + 5a 12+ 3a< -
9 - 12 3a< - 21 3 3 a < -7 - x + 3> 3 - x + x 3 > 3
true statement infinite solutions
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- - 5x < 5x- 25 - 5x + 24 5x 24 < -25 false statement no
solutions 6y- 3y 3y + 6 > 5y - 4 - 5y > 5y + 6 - 4 - 6 - 4-2y
+ 6> -2 Example 6: Solve the inequalities. 5x + 24 5y - 4 >
-10 -2y y < 5 -2
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- Example 7: Phone Company A charges an activation fee of 36
cents and then 3 cents per minute. Phone Company B charges 6 cents
per minute with no activation fee. For what value of x is Phone
Company A more expensive than Phone Company B?.36 +.03x >.06x
-.03x.36 >.03x 12 > x Phone Company A is more expensive when
the number of minutes is less than 12. If you talk for more than 12
minutes, Phone Company A is a good choice..03 x < 12
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- Example 8: Justin and Tyson are beginning an exercise program
to train for football season. Justin weighs 150 pounds and hopes to
gain 2 pounds per week. Tyson weighs 195 pounds and hopes to lose 1
pound per week. If the plan works, for how many weeks will Justin
weigh less than Tyson? JustinTyson 150 + 2x + 1x 150 + 3x < 195
- 150 3x < 45 x < 15 Justin will weigh less than Tyson up
until the 15 week mark. < 195 - 1x 33
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- Summary Essential Questions: How do we solve inequalities with
variables on both sides? When does an inequality have no solution
or a solution of all real numbers? Take 1 minute to write 2
sentences answering the essential question.