Question

Which of the following graphs shows the solution set for the inequality below

Answer 1

• Option C

Explanation:

`\sf |x+2|+7 > 10`

Move 7 to the right side:-

`\sf |x+2| > 10-7`

`\sf |x+2| > 3`

Now, we need to apply the absolute rule:-

`\sf x+2 > 3\:\: or \:\:-x-2 > 3`

`\sf x > 1\:\: or \:\:-x > 5`

`\sf x > 1\:\: or \:\: x < -5`

Therefore, C would be your answer!

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Answer 2

option C

Explanation:

Solving inequality with absolute value:

• Isolate absolute value expression.

I x + 2 I + 7 > 10

subtract 7 from both sides,

I x + 2 I + 7 - 7 > 10 - 7

Ix + 2I > 3

• Now, solve for both positive and negative versions of the inequality.
• Positive version,

x + 2 > 3

Subtract 2 from both sides,

x + 2 - 2 > 3 - 2

x > 1 is one of the solutions.

• Negative version,

Multiply the number after the inequality by (-1) and reverse the inequality sign.

x + 2 > 3

x + 2 < -3

Subtract 2 from both sides,

x + 2 - 2 < -3 -2

x < -5 is the other solutions.

x > 1 and x < - 5 are the solutions.

option C