Question

solve for g.
40 ≤ g - 8
write the solution as an inequality (for example, g > 9).
graph the solution.
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.
30 32 34 36 38 40 42 44 46 48 50
submit
work it out

Explanation:

Step1: Add 8 to both sides

To solve the inequality \( 40 \leq g - 8 \), we add 8 to both sides to isolate \( g \).

$$ 40 + 8 \leq g - 8 + 8 $$

Step2: Simplify both sides

Simplifying the left side \( 40 + 8 = 48 \) and the right side \( g - 8 + 8 = g \). So we get \( 48 \leq g \), which can also be written as \( g \geq 48 \)? Wait, no, wait: \( 40 + 8 = 48 \), so \( 48 \leq g \) is \( g \geq 48 \)? Wait, no, \( 40 \leq g - 8 \) adding 8 to both sides: \( 40 + 8 \leq g - 8 + 8 \) → \( 48 \leq g \), which is \( g \geq 48 \). Wait, but let's check again. The original inequality is \( 40 \leq g - 8 \). So we want to solve for \( g \), so add 8 to both sides: \( 40 + 8 \leq g \), so \( 48 \leq g \), which is \( g \geq 48 \). Wait, but let's verify with a number. If \( g = 48 \), then \( g - 8 = 40 \), and \( 40 \leq 40 \) is true. If \( g = 49 \), \( g - 8 = 41 \), and \( 40 \leq 41 \) is true. If \( g = 47 \), \( g - 8 = 39 \), and \( 40 \leq 39 \) is false. So yes, \( g \) must be greater than or equal to 48. Wait, but the number line has 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50. So the endpoint should be at 48, and the arrow pointing to the right (since \( g \geq 48 \)).

Wait, wait, I think I made a mistake. Let's re-express the inequality: \( 40 \leq g - 8 \). So \( g - 8 \geq 40 \). Then add 8 to both sides: \( g \geq 40 + 8 \), so \( g \geq 48 \). Yes, that's correct. So the solution is \( g \geq 48 \).

For the graph: We plot a closed dot at 48 (since the inequality is "greater than or equal to") and draw an arrow to the right (towards larger numbers) to represent all numbers greater than or equal to 48.

Answer:

The solution to the inequality \( 40 \leq g - 8 \) is \( g \geq 48 \). For the graph, plot a closed endpoint at 48 on the number line and draw an arrow pointing to the right (towards 50 and beyond).