Chapter 12 section 4
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Chapter 12 Section 4. Solving Multi-Step Inequalities. Example 1. Solve 9 + 3x < 27. Check your solution. 9 + 3x < 27 9 - 9 + 3x < 27 - 9 3x < 18 3 3 x < 6. Check. Substitute 6 and a number less than 6 into the inequality. Let x = 6 9 + 3( 6 ) < 27 9 + 18 < 27

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Chapter 12 Section 4

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Chapter 12 section 4

Chapter 12 Section 4

Solving Multi-Step Inequalities


Example 1

Example 1

Solve 9 + 3x < 27. Check your solution.

9 + 3x < 27

9 - 9 + 3x < 27 - 9

3x < 18

3 3

x < 6


Check

Check

Substitute 6 and a number less than 6 into the inequality.

Let x = 6

9 + 3(6) < 27

9 + 18 < 27

27 < 27

False,

The solution is {x l x < 6}.

Let x = 0

9 + 3(0) < 27

9 < 27

True


Your turn

Your Turn

Solve each inequality. Check your solution.

4 + 2x ≤ 12

{x l x ≤ 4}


Your turn1

Your Turn

Solve each inequality. Check your solution.

8x - 5 ≥ 11

{x l x ≥ 2}


Chapter 12 section 4

Solving inequalities is similar to solving equations. The only exception is that with inequalities, you must reverse the inequality symbol if you multiply or divide by a negitive number.


Example 3

Example 3

Solve -4x + 3 ≥ 23 + 6x. Check your solution.

-4x + 3 ≥ 23 + 6x

-4x – 6x + 3 ≥ 23 + 6x – 6x

-10x + 3 ≥ 23

-10x + 3 - 3≥ 23 – 3

-10x ≥ 20

-10 -10

x ≤ -2

Your solution is {x l x ≤ -2}. Check your solution.

Reverse the symbol


Your turn2

Your Turn

Solve each inequality. Check your solution.

10 – 5x < 25

{x l x > -3}


Your turn3

Your Turn

Solve each inequality. Check your solution.

3x + 1 > -17

{x l x < 6}


Example 4

Example 4

Solve 8 ≤ -2(x – 5). Check your solution.

8 ≤ -2(x – 5)

8 ≤ -2x + 10

8 - 10 ≤ -2x + 10 – 10

-2 ≤ -2x

-2 -2

1 ≥ x

The solution is {x l x ≤ 1). Check your solution.

Reverse the symbol


Your turn4

Your Turn

Solve each inequality. Check your solution.

2 > -(x + 7)

{x l x > -9}


Your turn5

Your Turn

Solve each inequality. Check your solution.

3(x – 4) ≤ x - 5

{x l x ≤ 3.5}


Chapter 12 section 4

Hannah’s scores on the first three of four 100 point tests were 85, 92, and 90. What score must she receive on the fourth test to have a mean score of more than 92 for all tests?

Explore

Let s = Hannah’s score on the fourth test.

The sum of Hannah’s four test scores, divided by 4, will give the mean score. The mean must be more than 92.


Chapter 12 section 4

Plan

The sum of Hannah’s four test scores, divided by 4, will give the mean score. The mean must be more than 92.


Solve

Solve

85 + 92+ 95+ s > 92

4

4 (85 + 92+ 95+ s)> 4(92)

4

85 + 92+ 95+ s > 368

267 - 267 + s > 368 - 267

s > 101


Examine

Examine

Substitute a number greater than 101, such as 102, into the original problem. Hannah’s average would be 92.25. Since 92.25 > 92 is a true statement, the solution is correct. Hannah’s must score more than 101 points out of a 100 point test. Without extra credit, this is not possible. So, Hannah cannot have a mean over 92.


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