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Which equation has only one solution?

|x – 5| = –1
|–6 – 2x| = 8
|5x + 10| = 10
|–6x + 3| = 0

Respuesta :

|5x+10| = 10

If you subtract 10 from each side to get |5x| = 0,

and 0 divided by 5 is equal to 0.

x=0

There is no such thing as -0, so this equation has only one solution.

The equation having only one solution is - [tex]|-6x+3|=0[/tex]

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 (|[tex]x[/tex]|) of a number?

The modulus of a number [tex]x[/tex] is given by -

                                                [tex]|x| =\left \{ {{-x \;\;\;for\;\;x < 0} \atop {x\;\;\;for\;\;x > 0}} \right.[/tex]

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[tex]x[/tex] +3) has one solution at [tex]x=\frac{1}{2}[/tex].

Hence, the equation having only one solution is :  |-6x+3|=0

To solve more problems on finding the solution of equation, visit the following link - https://brainly.com/question/12845011

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