What is the value of x?

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1 Answer
Jim G.
May 17, 2018

#x=10#

Explanation:

#"the line segment from A is an "color(blue)"angle bisector"#

#"let D be the point where it meets BC"#

#"then by the "color(blue)"Angle bisector theorem"#

#•color(white)(x)(AB)/(AC)=(BD)/(CD)#

#rArr8/12=(x+4)/(2x+1)#

#rArr2/3=(x+4)/(2x+1)larrcolor(blue)"cross-multiply"#

#rArr2(2x+1)=3(x+4)larrcolor(blue)"distribute"#

#rArr4x+2=3x+12#

#"subtract "3x" from both sides"#

#rArrx+2=12#

#"subtract 2 from both sides"#

#rArrx=12-2=10#

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