Math

QuestionFind the value of xx given PM=2x5P M=2 x-5, PN=6xP N=6 x, and MN=5x+4M N=5 x+4.

Studdy Solution

STEP 1

Assumptions1. PM =x -5. PN =6x3. MN =5x +4

STEP 2

In geometry, the segment addition postulate states that if a point B is between points A and C, then AB + BC = AC. In this case, point M is between points and N. Therefore, we can write the equationPM+MN=PNPM + MN = PN

STEP 3

Substitute the given expressions for PM, PN, and MN into the equation from2.
(2x5)+(5x+)=6x(2x -5) + (5x +) =6x

STEP 4

implify the left side of the equation by combining like terms.
7x1=6x7x -1 =6x

STEP 5

To solve for x, we need to isolate x on one side of the equation. Subtractx from both sides of the equation.
7xx=xx+17x -x =x -x +1

STEP 6

implify both sides of the equation.
x=1x =1The value of x is1.

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