B is the midpoint of AC. If Ab= x +5 and BC = 2x-11, find the measure of Ab.
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__________________________ Measurement of "AC" : (x + 5) + (2x <span>− 11) ; ________________________ Find the measurement of "AB" [which is: "(x+5)" ]: ______________________________________________ First, simplify to find the measurement of "AC" : ________________________________________ </span>(x + 5) + (2x − 11) ; = (x + 5) + 1(2x − 11) ; = x + 5 + 2x − 11 ; → Combine the "like terms" ; x + 2x = 3x ; 5 − 11 = - 6 ; ______________ to get: 3x − 6 ; _______________ So, (x + 5) + (2x − 11) = 3x − 6 ; _______________________________ Solve for: "(x + 5)" _______________________________ We have: _______________________________ (x + 5) + (2x − 11) = 3x − 6 ; Subtract: "(2x − 11)" ; from EACH SIDE of the equation ; to isolate "(x + 5)" on one side of the equation; and to solve for "(x + 5)" ; ________________________________________________________ → (x + 5) + (2x − 11) − (2x − 11) = (3x − 6) − (2x − 11) ; → (x + 5) = (3x − 6) − (2x − 11) ; _________________________________________________ Note: Simplify: "(3x − 6) − (2x − 11)" ; → (3x − 6) − (2x − 11) ; = (3x − 6) − 1(2x − 11) ; = 3x − 6 − 2x + 11 ; __________________________ → Combine the "like terms" : _____________________________ +3x − 2x = 1x = x ; -6 + 11 = 5 ; _____________________________ To get: x + 5 ; So we have: ______________________________ x + 5 = x + 5 ; ______________________________ So, x = all real numbers. x = <span>ℝ </span>
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