Question

Two segments are combined. The first segment has a length 2X +1. The second segment has a length 3X +4. The second segment is two times the length of the first segment. Find the value of X by setting up and solving an equation.

Answer 1

Let's first draw the scenario to better understand the question.

Equation of segment A = 2x + 1

Equation of segment B = 3x + 4

It also says that the second segment is two times the length of the first segment.

We will use that relationship to find x.

`\text{ Length of segment B = 2 x Length of segment A}`
`\text{ 3x + 4 = 2\lparen2x + 1\rparen}`
`\text{ 3x + 4 = 4x + 2}`
`\text{ 3x - 4x = 2 - 4}`
`\text{ -x = -2}`
`\text{ }(-x)/(-1)\text{ = }(-2)/(-1)`
`\text{ x = 2}`

Therefore, x = 2