Math Journal 10-16

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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.

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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.
• 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 + 55 6x + 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.
Summary