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Question
What values of x will make DE || AB in the given figure?
Solution
If `DE|| AB`, then
`(CE)/(CB)=(CD)/(AC)`
`X/(X+3x+4)=(x+3)/(4x+22)`
`x/(4x+4)=(x+3)/(4x+22)`
`x xx(4x+22)=xx+3xx(4x+4)`
`4x^2+22x=4x^2+12x+4x+12`
`cancel(4x^2)+22x=cancel(4x^2)+12+4x+12`
`22x=16x+12`
`22x-16x=12`
`6x=12`
`x=12/6`
`x=2`
Hence, the value of x is 2.
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