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Math Journal 10-16 PowerPoint PPT Presentation


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Math Journal 10-16. Rearrange the equation so that y is a function of x 2. Solve for x. 3. 4. Math Journal 10-15. Solve the formula for the given variable. 2. Solve for x. 3. 4. Unit 3 Day 7: Solving Inequalities with Variables on Both Sides.

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Math Journal 10-16

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Math journal 10 16

Math Journal 10-16

Rearrange the equation so that y is a function of x

  • 2.

  • Solve for x.

  • 3. 4.


Math journal 10 16

Math Journal 10-15

Solve the formula for the given variable.

  • 2.

  • Solve for x.

  • 3. 4.


Math journal 10 16

  • 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?


Vocabulary

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


Math journal 10 16

  • x

  • x

  • < 1

  • > 4

  • 9

  • 9

  • 9

  • 9

  • 9x

  • 9x

  • > 36

  • < 9

  • Example 1: Solve the inequalities.

  • 7x + 19 > -2x + 556x + 22 < -3x + 31

  • 9x

  • 9x

  • + 19

  • + 22

  • > 55

  • < 31

  • + 2x

  • + 2x

  • + 3x

  • + 3x

  • - 19

  • -19

  • - 22

  • -22


Math journal 10 16

  • -2

  • 1

  • -2

  • 2

  • -12

  • -12

  • Example 2: Solve the inequalities.

  • x + 2 > 3x + 1-8x + 7 < 4x – 5

  • -12x

  • < -12

  • -2x

  • > -1

  • x <

  • -2x + 2

  • > 1

  • -12x + 7

  • < - 5

  • - 3x

  • - 3x

  • - 4x

  • - 4x

  • - 7

  • - 7

  • - 2

  • - 2

  • x > 1


Math journal 10 16

  • -3x

  • + 4

  • -6

  • -6

  • 4

  • -6x

  • < 12

  • 1

  • -6x + 4

  • < 16

  • Example 3: Solve the inequality.

  • (-12x + 16) < 10 – 3(-x – 2)

  • -3x

  • + 4

  • + 3x

  • + 6

  • < 10

  • < 16

  • + 3x

  • - 3x

  • - 3x

  • - 4

  • - 4

  • x > -2


Math journal 10 16

  • 16x

  • < 16

  • 2

  • 16

  • 16

  • Example 4: Solve the inequality.

  • (12x – 4) < 2(7 – 5x)

  • 1

  • 16x

  • - 2

  • < 14

  • 6x

  • - 2

  • < 14

  • - 10x

  • + 10x

  • + 10x

  • + 2

  • + 2

  • x < 1


Math journal 10 16

  • 3

  • 3

  • - x

  • + 3

  • > 3

  • Example 5: Solve the inequalities.

  • 12 – 2a < - 5a – 9 x – 2x + 3 > 3 – x

  • 3a

  • < - 21

  • > 3

  • 3

  • 12

  • + 3a

  • < - 9

  • + 5a

  • + 5a

  • - x

  • + x

  • + x

  • - 12

  • - 12

  • true statement

  • infinite solutions

  • a < -7


Math journal 10 16

  • > 5y

  • - 4

  • + 6

  • -2y

  • 5x

  • > -10

  • < -25

  • - 4

  • + 24

  • > 5y

  • 24

  • -2

  • -2

  • Example 6: Solve the inequalities.

  • 5x + 24 < 5(x - 5) 6y - (3y - 6) > 5y - 4

  • -2y + 6

  • >

  • - 4

  • < 5x

  • - 25

  • + 6

  • 6y

  • - 3y

  • - 5x

  • - 5x

  • 3y

  • - 5y

  • - 5y

  • false statement

  • no solutions

  • - 6

  • - 6

  • y < 5


Math journal 10 16

  • .03

  • .03

  • .36 > .03x

  • 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

  • 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.

  • - .03x

  • - .03x

  • 12 > x

  • x < 12


Math journal 10 16

  • 3

  • 3

  • 150 + 3x < 195

  • 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?

  • 3x < 45

  • Justin

  • Tyson

  • < 195 - 1x

  • 150 + 2x

  • + 1x

  • + 1x

  • Justin will weigh less than Tyson up until the 15 week mark.

  • - 150

  • - 150

  • x < 15


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.

Summary


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