Question
Should the point be open or closed? and Where is the shading? for 5x - 2 ≤ 8
Answers
GPT 3.5
To determine whether the point should be open or closed, and to find the shading, we need to solve the inequality 5x - 2 ≤ 8.
First, we can add 2 to both sides of the inequality:
5x - 2 + 2 ≤ 8 + 2
5x ≤ 10
Next, we divide both sides by 5 to isolate x:
5x/5 ≤ 10/5
x ≤ 2
Since the inequality states "less than or equal to," the point should be closed. We represent this with a solid dot on the number line at x = 2.
To indicate the shading, we shade all the values of x that satisfy the inequality. In this case, since x can be any value less than or equal to 2, we shade to the left of the solid dot on the number line.
So, the point is closed, and the shading is to the left of x = 2.
First, we can add 2 to both sides of the inequality:
5x - 2 + 2 ≤ 8 + 2
5x ≤ 10
Next, we divide both sides by 5 to isolate x:
5x/5 ≤ 10/5
x ≤ 2
Since the inequality states "less than or equal to," the point should be closed. We represent this with a solid dot on the number line at x = 2.
To indicate the shading, we shade all the values of x that satisfy the inequality. In this case, since x can be any value less than or equal to 2, we shade to the left of the solid dot on the number line.
So, the point is closed, and the shading is to the left of x = 2.