The equation having only one solution is - \(|-6x+3|=0\)
We have the following equations -
|x – 5| = –1
|–6 – 2x| = 8
|5x + 10| = 10
|–6x + 3| = 0
We have to find the equation which only has one solution.
What is Modulus (|\(x\)|) of a number?
The modulus of a number \(x\) is given by -
\(|x| =\left \{ {{-x \;\;\;for\;\;x < 0} \atop {x\;\;\;for\;\;x > 0}} \right.\)
Using the above property, we can find out the number of solutions of any modulus equation.
|x-5| = - 1
(x-5) = 1 and (x-5) = -1
|-6-2x |= -1
(-6-2x) = -8 and (-6-2x) = 8
|5x +10|=10
(5x+10)= 10 and (5x+10)= -10
|-6x+3|=0
(-6x+3)= 0 and (-6x+3) = -0 or (-6x+3)= 0
It can be seen from the above solutions that except equation |-6x + 3|, all the equations have two solutions. Only Equation - (-6\(x\) +3) has one solution at \(x=\frac{1}{2}\).
Hence, the equation having only one solution is : |-6x+3|=0
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