Question

Solving Linear Inequalities

Video Player

00:0303:05

Show Transcript
Question 1

When multiplying or dividing by a negative number, the inequality sign must be ___.
Responses

A removedremoved

B flippedflipped
Question 2

The solution to the problem -4(x - 3) ≤ 16 is that x is greater than or equal to ___.
Responses

A 11

B -1-1
Question 3

Does the second problem have a solution?
Responses

A YesYes

B No

Answer 1

Let's go through the questions one by one:

**Question 1**
When multiplying or dividing by a negative number, the inequality sign must be ___.
- The correct answer is **B** flipped. When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

---

**Question 2**
The solution to the problem -4(x - 3) ≤ 16 is that x is greater than or equal to ___.
- First, let's solve the inequality step by step.
1. Distribute the -4:
\(-4x + 12 \leq 16\)
2. Subtract 12 from both sides:
\(-4x \leq 4\)
3. Divide both sides by -4 and remember to flip the inequality sign:
\(x \geq -1\)
So, the correct answer is **B** -1.

---

**Question 3**
Does the second problem have a solution?
- As we have solved it in Question 2, the solution exists (x is greater than or equal to -1). Hence, the correct answer is **A** Yes.

---

So your answers would be:
1. B
2. B
3. A