Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

What is the solution to [tex]|2x - 8| \ \textless \ 2[/tex]?

A. [tex]3 \ \textless \ x \ \textless \ 5[/tex]
B. [tex]-5 \ \textless \ x \ \textless \ -3[/tex]
C. [tex]x \ \textgreater \ 5[/tex] or [tex]x \ \textless \ 3[/tex]
D. [tex]x \ \textgreater \ -3[/tex] or [tex]x \ \textless \ -5[/tex]

Sagot :

GinnyAnswer
To solve the inequality [tex]\( |2x - 8| < 2 \)[/tex], let's break it down step-by-step:

1. The absolute value inequality [tex]\( |2x - 8| < 2 \)[/tex] means that the expression [tex]\( 2x - 8 \)[/tex] lies within the range of -2 and 2. This can be rewritten as two separate inequalities:

[tex]\[ -2 < 2x - 8 < 2 \][/tex]

2. We now need to solve these two inequalities separately. First, let's deal with the left inequality:

[tex]\[ -2 < 2x - 8 \][/tex]

Add 8 to both sides to isolate the term involving [tex]\( x \)[/tex]:

[tex]\[ -2 + 8 < 2x \][/tex]

[tex]\[ 6 < 2x \][/tex]

Now, divide both sides by 2 to solve for [tex]\( x \)[/tex]:

[tex]\[ 3 < x \][/tex]

So, one part of the solution is:

[tex]\[ x > 3 \][/tex]

3. Now, let's deal with the right inequality:

[tex]\[ 2x - 8 < 2 \][/tex]

Again, add 8 to both sides:

[tex]\[ 2x - 8 + 8 < 2 + 8 \][/tex]

[tex]\[ 2x < 10 \][/tex]

Divide by 2:

[tex]\[ x < 5 \][/tex]

So, the other part of the solution is:

[tex]\[ x < 5 \][/tex]

4. Combining these two parts, we get the solution to the inequality:

[tex]\[ 3 < x < 5 \][/tex]

So, the correct answer is:

A. [tex]\( 3 < x < 5 \)[/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.