EXAMPLE 9 Solve: -4 < 2(x – 1) S 4. Write the solution set in interval notation and graph it. Strategy We will use properties of inequality to isolate the variable by itself as the middle part of the inequality. Why To solve the original inequality, we want to find a simpler equivalent inequality of the form a number < xs a number, whose solution is obvious. Solution -4 < 2(x – 1)S 4 -4 < 2x - This is the compound inequality to solve. Distribute the multiplication by 2. -4 + 2 < 2x - + 2 5 4 + 2 To isolate 2x, undo the subtraction of 2 by adding 2 to all three parts. < 2x S 6 Do the additions. 2x To isolate x, we undo the multiplication by 2 by dividing all three parts by 2. 2 2 2 O
EXAMPLE 9 Solve: -4 < 2(x – 1) S 4. Write the solution set in interval notation and graph it. Strategy We will use properties of inequality to isolate the variable by itself as the middle part of the inequality. Why To solve the original inequality, we want to find a simpler equivalent inequality of the form a number < xs a number, whose solution is obvious. Solution -4 < 2(x – 1)S 4 -4 < 2x - This is the compound inequality to solve. Distribute the multiplication by 2. -4 + 2 < 2x - + 2 5 4 + 2 To isolate 2x, undo the subtraction of 2 by adding 2 to all three parts. < 2x S 6 Do the additions. 2x To isolate x, we undo the multiplication by 2 by dividing all three parts by 2. 2 2 2 O
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![EXAMPLE 9
Solve: -4 < 2(x – 1) < 4. Write the solution set in interval notation and graph it.
Strategy
We will use properties of inequality to isolate the variable by itself as the middle
part of the inequality.
Why
To solve the original inequality, we want to find a simpler equivalent inequality of
the form a number < x < a number, whose solution is obvious.
Solution
-4 < 2(x – 1)< 4
-4 < 2x - < 4
This is the compound inequality to solve.
Distribute the multiplication by 2.
-4 + 2 < 2x –
+ 2 < 4 + 2
To isolate 2x, undo the subtraction of 2 by adding 2 to all three parts.
< 2x < 6
Do the additions.
2x
To isolate x, we undo the multiplication by 2 by dividing all three parts by 2.
2
< x < 3
The solution set is (-1, 3] and its graph is shown.
Do the divisions.
-2 -1 0
3
4
Self Check 9
Solve: -15 < 3(t + 3) < 15. Write the solution set in interval notation.
Graph the solution set.
O(IV)
2
-8
2
O(III)
O(I)
-8
O(II)
-8
2
-8
이2
VI](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c69c300-2450-4b46-97af-8596007e11b9%2Ff4b360d9-6836-4f24-8615-71a6de00a34f%2Fzxg52ed_processed.png&w=3840&q=75)
Transcribed Image Text:EXAMPLE 9
Solve: -4 < 2(x – 1) < 4. Write the solution set in interval notation and graph it.
Strategy
We will use properties of inequality to isolate the variable by itself as the middle
part of the inequality.
Why
To solve the original inequality, we want to find a simpler equivalent inequality of
the form a number < x < a number, whose solution is obvious.
Solution
-4 < 2(x – 1)< 4
-4 < 2x - < 4
This is the compound inequality to solve.
Distribute the multiplication by 2.
-4 + 2 < 2x –
+ 2 < 4 + 2
To isolate 2x, undo the subtraction of 2 by adding 2 to all three parts.
< 2x < 6
Do the additions.
2x
To isolate x, we undo the multiplication by 2 by dividing all three parts by 2.
2
< x < 3
The solution set is (-1, 3] and its graph is shown.
Do the divisions.
-2 -1 0
3
4
Self Check 9
Solve: -15 < 3(t + 3) < 15. Write the solution set in interval notation.
Graph the solution set.
O(IV)
2
-8
2
O(III)
O(I)
-8
O(II)
-8
2
-8
이2
VI
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