slide1
Download
Skip this Video
Download Presentation
Math Journal 10-16

Loading in 2 Seconds...

play fullscreen
1 / 13

Math Journal 10-16 - PowerPoint PPT Presentation


  • 65 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Math Journal 10-16' - bevis-solomon


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Math Journal 10-16

Rearrange the equation so that y is a function of x

  • 2.
  • Solve for x.
  • 3. 4.
slide2

Math Journal 10-15

Solve the formula for the given variable.

  • 2.
  • Solve for x.
  • 3. 4.
slide3

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
slide5

x

  • x
  • < 1
  • > 4
  • 9
  • 9
  • 9
  • 9
  • 9x
  • 9x
  • > 36
  • < 9
  • Example 1: Solve the inequalities.
  • 7x + 19 > -2x + 55 6x + 22 < -3x + 31
  • 9x
  • 9x
  • + 19
  • + 22
  • > 55
  • < 31
  • + 2x
  • + 2x
  • + 3x
  • + 3x
  • - 19
  • -19
  • - 22
  • -22
slide6

-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
slide7

-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
slide8

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
slide9

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
slide10

> 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
slide11

.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
slide12

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
ad