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# Math Journal 10-16 PowerPoint PPT Presentation

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.

Math Journal 10-16

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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

• 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

• 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

• 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

• -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

• -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

• 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

• 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

• > 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

• .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

• 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

• 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.