Question

Find MK. ML = 8, LK = x + 2, MK = 4x - 2

Answer 1

From the given description, it appears that M, L, and K are collinear and the length of MK is equal to the sum of ML and LK.

To be able to find the length of MK let's first find the value of x using the equation of the sum of the lines.

`\text{ }\bar{\text{ML}}\text{ + }\bar{\text{LK}}\text{ = }\bar{\text{MK}}`

Let's plug in the values given in the description.

`\text{ (8) + (x + 2) = 4x - 2}`
`\text{ 8 + x + 2 = 4x - 2}`
`\text{ x + 10 = 4x - 2}`
`\text{ x - 4x = -2 - 10}`
`\text{ -3x = -12}`
`\text{ }\frac{\text{-3x}}{-3}\text{ = }\frac{\text{-12}}{-3}`
`\text{ x = 4}`

Let's plug in x = 4 in the equation for the length of MK = 4x - 2.

`\text{ }\bar{\text{MK}}\text{ = 4x - 2}`
`\text{ }\bar{\text{MK}}\text{ = 4(4) - 2}`
`\text{ }\bar{\text{MK}}\text{ = 16 - 2}`
`\text{ }\bar{\text{MK}}\text{ = 1}4`

Therefore, the length of MK is 14.