Solve the inequality. Graph the solution set and write it in interval notation.

Question

−3(x−4)−6x
<
−(4x+2)+2x

Question content area bottom
Part 1
Choose the correct graph below.
A.
An infinite number line has a tick mark labeled 0. The region to the right of a left bracket labeled 2 is shaded.
02
B.
An infinite number line has a tick mark labeled 0. The region to the right of a left parenthesis labeled 2 is shaded.
02
Your answer is correct.
C.
An infinite number line has a tick mark labeled 0. The region to the left of a right bracket labeled 2 is shaded.
02
D.
An infinite number line has a tick mark labeled 0. The region to the left of a right parenthesis labeled 2 is shaded.
02
Part 2
Write the answer in interval notation.

Answer 1

The correct answer is:

A. An infinite number line has a tick mark labeled 0. The region to the right of a left bracket labeled 2 is shaded (02).

The solution set in interval notation is:

(2, ∞)

Answer 2

The perimeter of a rectangle is to be no greater than
60 centimeters and the length must be
25 centimeters. Find the maximum width of the rectangle.

x cm25 cm
Question content area bottom
Part 1

the perimeter
of the rectangle
is less than or equal to
60
↓
↓
↓
x+25+
enter your response here
▼

60

​First, understand the problem. Then translate the statement into an inequality.

Answer 3

The perimeter of a rectangle is given by the formula P = 2(length + width).

In this case, the length is fixed at 25 cm.

We want the perimeter to be no greater than 60 cm.

So, the inequality representing this situation would be:

2(25 + width) ≤ 60

Simplifying, we get:

50 + 2width ≤ 60

Subtracting 50 from both sides:

2width ≤ 10

Dividing both sides by 2:

width ≤ 5

Therefore, the maximum width of the rectangle can be 5 cm.