Question

70 POINTS!!!! 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)

Answer 1

Answer:

$\textsf{A.} \quad x < -4$

B.   To graph the solution to the inequality on number line, place an open circle at -4 and shade to the left of the circle.

C.   x = -5, x = -6

Step-by-step explanation:

Given inequality:

$-6(x-3) > 42$

Part A

To solve the inequality, divide both sides by -6 (remembering to reverse the inequality symbol as we are dividing by a negative number):

$\implies \dfrac{-6(x-3)}{-6} > \dfrac{42}{-6}$

$\implies x-3 < -7$

Add 3 to both sides:

$\implies x-3+3 < -7+3$

$\implies x < -4$

Part B

When graphing an inequality on a number line:

• < or > : open circle.
• ≤ or ≥ : closed circle.
• < or ≤ : shade to the left.
• > or ≥ : shade to the right.

To graph the solution to the inequality on number line, place an open circle at -4 and shade to the left of the circle.

(See the attachment for the solution graphed on a number line).

Part C

Two values that would make the inequality true, are any values of x that are less than -4.  For example:

• x = -5
• x = -6

We know the two values are solutions to the inequality as they are both included in the shaded part of the solution represented on the number line (from part B).