Solve and graph this inequality: −3x−1≥11
Write your solved inequality here: Should the point be open or closed? Where is the shading?
To solve the inequality −3x−1≥11, we first need to isolate the variable x.
Adding 1 to both sides of the inequality gives us:
−3x−1 + 1 ≥ 11 + 1
Simplifying further, we get:
−3x ≥ 12
Next, we divide both sides of the inequality by −3. Since we are dividing by a negative number, the inequality sign will flip:
−3x/−3 ≤ 12/−3
Simplifying, we have:
x ≤ -4
So, the inequality −3x−1≥11 is equivalent to x ≤ -4.
To graph this inequality, we would represent all values of x that are less than or equal to -4 on a number line.
To determine if the point should be open or closed, we consider the equal sign in the inequality. Since the inequality is ≤ (less than or equal to), the point on the number line representing -4 should be closed, denoted by a filled-in circle.
The shading on the number line would be to the left of -4, as the inequality states that x must be less than or equal to -4.