The inequality −6(x − 3) > 42 is given.
Part A: Solve the inequality and show every step of your work. (4 points)
Part B: Explain in words how to graph the solution to the inequality on a number line. (4 points)
Part C: Find two values that would make the inequality true. Explain how you know the values are solutions to the inequality. (4 points)
Part A:
-6(x - 3) > 42
Distribute -6 to both terms inside the parentheses:
-6x + 18 > 42
Subtract 18 from both sides:
-6x > 24
Divide both sides by -6 (remember to flip the inequality sign when dividing by a negative number):
x < -4
Part B:
To graph the solution to the inequality on a number line:
1. Mark a point at -4 on the number line.
2. Draw an arrow to the left to indicate that all values less than -4 are solutions to the inequality.
Part C:
Two values that would make the inequality true are x = -5 and x = -10.
For x = -5:
-6(-5 - 3) > 42
-6(-8) > 42
48 > 42 (True)
For x = -10:
-6(-10 - 3) > 42
-6(-13) > 42
78 > 42 (True)
Both values satisfy the inequality and make it true.