Question

11) AN= 2x - 6 and NB = 5x +4. The total length of AB = 82. What is the value of x?What is the length of AN ? What is the length of NB ? Please show all work

Answer 1

Notice that:

`AB=AN+NB,`

substituting AN=2x-6, AB=82, and NB=5x+4 we get:

`82=2x-6+5x+4.`

Adding like terms we get:

`82=7x-2.`

Adding 2 to the above equation we get:

`\begin{gathered} 82+2=7x-2+2, \\ 84=7x\text{.} \end{gathered}`

Dividing the above equation by 7 we get:

`\begin{gathered} (84)/(7)=(7x)/(7), \\ 12=x\text{.} \end{gathered}`

Now, substituting x=12 in AN=2x-6 we get:

`\begin{gathered} AN=2\cdot12-6, \\ AN=24-6, \\ AN=18. \end{gathered}`

Finally, substituting x=12 in NB=5x+4 we get:

`\begin{gathered} NB=5\cdot12+4, \\ NB=60+4, \\ NB=64. \end{gathered}`

Answer:

`\begin{gathered} x=12, \\ AN=18, \\ NB=64. \end{gathered}`