1. Two segments are combined. The first segment has length 2x + 1. The second segment

has length 3x + 4. The fecond segment is 2 times the length of the first segment. Find the

value of x by setting up and solving an equation. (6 points)

equation => 3x + 4 = 2(2x + 1)

The value of x is 2

Step-by-step explanation:

The first segment has length 2x + 1.

The second segment has length 3x + 4.

The second segment is 2 times the length of the first segment.  We are asked to find the value of x by setting up and solving an equation.

The corresponding equations is,

3x + 4 = 2(2x + 1)

Since the second segment is 2 times the length of the first segment

3x + 4 = 4x + 2

Combine like terms

3x - 4x = 2 - 4

-x = -2

Multiply both sides by -1

x = 2

Therefore, the value of x is 2

Bonus:

The length of the first segment is

First segment = 2x + 1

First segment = 2(2) + 1

First segment = 4 + 1

First segment = 5

The length of the second segment is

Second segment = 3x + 4

Second segment = 3(2) + 4

Second segment = 6 + 4

Second segment = 10