Question

solve for ( x ) and graph the solution on the number line below.

( -x - 3 geq -2 ) or ( -x - 3 leq -9 )

answer attempt 1 out of 3

inequality notation:

number line:

Explanation:

Step1: Solve the first inequality \(-x - 3\geq - 2\)

Add \(3\) to both sides:
\(-x-3 + 3\geq - 2+3\)
\(-x\geq1\)
Multiply both sides by \(- 1\) and reverse the inequality sign:
\(x\leq - 1\)

Step2: Solve the second inequality \(-x - 3\leq - 9\)

Add \(3\) to both sides:
\(-x-3 + 3\leq - 9+3\)
\(-x\leq - 6\)
Multiply both sides by \(-1\) and reverse the inequality sign:
\(x\geq6\)

Answer:

Inequality Notation: \(x\leq - 1\) or \(x\geq6\)

For the number - line:

• For \(x\leq - 1\), draw a closed circle at \(-1\) (because the inequality includes equality) and shade to the left.
• For \(x\geq6\), draw a closed circle at \(6\) (because the inequality includes equality) and shade to the right.