Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

What is the solution to the inequality [tex]|2x + 3| \ \textless \ 7[/tex]?

A. [tex]4 \ \textless \ x \ \textless \ 10[/tex]
B. [tex]-5 \ \textless \ x \ \textless \ 2[/tex]
C. [tex]x \ \textless \ 4[/tex] or [tex]x \ \textgreater \ 10[/tex]
D. [tex]x \ \textless \ -5[/tex] or [tex]x \ \textgreater \ 2[/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve the given inequality [tex]\( |2x + 3| < 7 \)[/tex] step-by-step.

### Step 1: Understand the Inequality

The absolute value inequality [tex]\( |2x + 3| < 7 \)[/tex] can be broken down into two separate linear inequalities:

[tex]\[ -7 < 2x + 3 < 7 \][/tex]

### Step 2: Break it Down

We can express [tex]\( |2x + 3| < 7 \)[/tex] as a compound inequality:

[tex]\[ -7 < 2x + 3 \quad \text{and} \quad 2x + 3 < 7 \][/tex]

### Step 3: Solve the Compound Inequality

#### Part 1: Solve [tex]\( -7 < 2x + 3 \)[/tex]

First, isolate [tex]\( x \)[/tex]:

1. Subtract 3 from both sides:
[tex]\[ -7 - 3 < 2x \][/tex]
[tex]\[ -10 < 2x \][/tex]

2. Divide both sides by 2:
[tex]\[ -5 < x \][/tex]

#### Part 2: Solve [tex]\( 2x + 3 < 7 \)[/tex]

Next, isolate [tex]\( x \)[/tex]:

1. Subtract 3 from both sides:
[tex]\[ 2x < 7 - 3 \][/tex]
[tex]\[ 2x < 4 \][/tex]

2. Divide both sides by 2:
[tex]\[ x < 2 \][/tex]

### Step 4: Combine the Solutions

From both parts, we obtained:

[tex]\[ -5 < x \][/tex]
[tex]\[ x < 2 \][/tex]

Combining these results, we get:

[tex]\[ -5 < x < 2 \][/tex]

### Step 5: Write the Final Solution

Therefore, the solution to the inequality [tex]\( |2x + 3| < 7 \)[/tex] is:

[tex]\[ -5 < x < 2 \][/tex]

### Step 6: Find the Correct Choice

Looking at the given options, the correct choice is:

[tex]\[ \boxed{-5 < x < 2} \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.