Questions: Solve the inequality for x and identify the graph of its solution. x+1>2 Choose the answer that gives both the correct solution and the correct graph. A. Solution: x<-3 or x>1 B. Solution: x>-3 and x<1 C. Solution: x>-1 and x<3

Solution Steps

The given inequality is \(|x + 1| > 2\). This is an absolute value inequality, which means we need to consider two cases: one where the expression inside the absolute value is greater than 2, and one where it is less than -2.

We split the inequality \(|x + 1| > 2\) into two separate inequalities:

1. \(x + 1 > 2\)
2. \(x + 1 < -2\)

Solve each of the inequalities separately:

1. \(x + 1 > 2\)
   • Subtract 1 from both sides: \(x > 1\)
2. \(x + 1 < -2\)
   • Subtract 1 from both sides: \(x < -3\)

The solutions to the inequalities are \(x > 1\) and \(x < -3\). This means \(x\) can be any value greater than 1 or any value less than -3.

The correct graph will show two separate regions: one where \(x\) is greater than 1 and one where \(x\) is less than -3.

Final Answer