Question

question
solve for ( x ) and graph the solution on the number line below.
( -x - 1 geq -3 ) or ( -6 geq -x - 1 )
answer attempt 1 out of 3
inequality notation:
number line:

Explanation:

Step1: Solve first inequality \(-x - 1 \geq -3\)

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

Step2: Solve second inequality \(-6 \geq -x - 1\)

Add 1 to both sides: \(-6 + 1 \geq -x - 1 + 1\)
Simplify: \(-5 \geq -x\)
Multiply both sides by -1 (reverse inequality): \(5 \leq x\) or \(x \geq 5\)

Step3: Combine solutions (or)

The solutions are \(x \leq 2\) or \(x \geq 5\)

Answer:

Inequality Notation: \(x \leq 2\) or \(x \geq 5\)

(For the number line: Plot a closed circle at 2 and shade to the left, plot a closed circle at 5 and shade to the right.)