Answered

Get expert insights and community support for your questions on IDNLearn.com. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.

Solve the inequality for [tex]$x$[/tex] and identify the graph of its solution.

[tex] |x+2|\ \textgreater \ 2 [/tex]

Choose the answer that gives both the correct solution and the correct graph.

A. Solution: [tex]x\ \textgreater \ 0[/tex] and [tex]x\ \textless \ 4[/tex]

B. Solution: [tex]x\ \textless \ -4[/tex] or [tex]x\ \textgreater \ 0[/tex]

C. Solution: [tex]x\ \textgreater \ -4[/tex] and [tex]x\ \textless \ 0[/tex]

D. Solution: [tex]x\ \textless \ -4[/tex] or [tex]x\ \textgreater \ 0[/tex]

Sagot :

GinnyAnsweridn
Let's solve the inequality [tex]\( |x+2| > 2 \)[/tex] step by step.

### Step 1: Understand the Absolute Value Inequality
The inequality [tex]\( |x+2| > 2 \)[/tex] can be broken down into two separate inequalities:
1. [tex]\( x + 2 > 2 \)[/tex]
2. [tex]\( x + 2 < -2 \)[/tex]

### Step 2: Solve Each Inequality Separately
#### Solve [tex]\( x + 2 > 2 \)[/tex]
[tex]\[ x + 2 > 2 \][/tex]
Subtract 2 from both sides:
[tex]\[ x > 0 \][/tex]

#### Solve [tex]\( x + 2 < -2 \)[/tex]
[tex]\[ x + 2 < -2 \][/tex]
Subtract 2 from both sides:
[tex]\[ x < -4 \][/tex]

### Step 3: Combine the Solutions
The solutions from both inequalities are [tex]\( x > 0 \)[/tex] and [tex]\( x < -4 \)[/tex].

### Step 4: Interpret the Combined Solution
The inequality [tex]\( |x+2| > 2 \)[/tex] is satisfied when [tex]\( x \)[/tex] is either greater than 0 or less than -4.

### Step 5: Choose the Correct Answer and Graph
The correct solution range is [tex]\( x > 0 \)[/tex] or [tex]\( x < -4 \)[/tex].

Checking the options:
- Option D: Solution: [tex]\( x < -4 \)[/tex] or [tex]\( x > 0 \)[/tex]

Thus, the correct answer is:
D. Solution: [tex]\( x < -4 \)[/tex] or [tex]\( x > 0 \)[/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.