Question

solve the inequality and graph the solution.
1 ≥ g - 2
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
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Explanation:

Step1: Isolate the variable \( g \)

To solve the inequality \( 1 \geq g - 2 \), we add 2 to both sides of the inequality. This is based on the addition property of inequalities, which states that adding the same number to both sides of an inequality does not change the direction of the inequality sign.
So, \( 1 + 2 \geq g - 2 + 2 \)
Simplifying both sides, we get \( 3 \geq g \), or equivalently \( g \leq 3 \).

Step2: Graph the solution

For the inequality \( g \leq 3 \), the endpoint is at 3 (and it is a closed circle because the inequality is "less than or equal to", meaning 3 is included in the solution set). The arrow points to the left (towards negative infinity) because we are looking for all values of \( g \) that are less than or equal to 3. On the given number line, we plot a closed circle at 3 and draw an arrow to the left.

Answer:

The solution to the inequality \( 1 \geq g - 2 \) is \( g \leq 3 \). To graph it, plot a closed circle at 3 on the number line and draw an arrow pointing to the left.