Solve and graph this inequality: Write your solved inequality here: (Do NOT round. Leave your answer as a reduced fraction.) 5(-3x -2) ≥ - 15 Open or closed
The given inequality is 5(-3x - 2) ≥ -15.
First, distribute 5 to the expression inside the parentheses:
-15x - 10 ≥ -15.
Next, add 10 to both sides of the inequality:
-15x ≥ -15 + 10,
which simplifies to -15x ≥ -5.
Divide both sides of the inequality by -15. Remember to reverse the inequality sign when dividing by a negative number:
x ≤ -5/-15.
Simplifying the right side gives x ≤ 1/3.
The solution to the inequality is x ≤ 1/3.
To graph the inequality, draw a number line and mark a closed circle at the point 1/3, indicating that it is included in the solution. Then, shade all the numbers to the left of 1/3, since they satisfy the inequality.
The graph of the inequality x ≤ 1/3 should look like this:
<---|======o------------>
-∞ 1/3