If the equation given a unique and single value of variable after solving then the equation is said one solution equation.
The equation which has only one solution are,
[tex]5x+3=-2(2x+3)[/tex]
Thus, the option C is the correct option.
How to find one solution of equation?
If the equation given a unique and single value of variable after solving then the equation is said one solution equation.
Such equation gives exactly one solution.
Given information-
To find the equation we have to solve each equation one by one.
- A)The equation given in the problem is,
[tex]-7x+2&=-3(x-3)-4x-7\\[/tex]
Solve it further,
[tex]-7x+2&=-3x+9-4x-7\\-7x+2&=-7x+2\\.\;\;\;\;\;\;\;\;\;\;\;0=0[/tex]
Thus this equation has no solution. Hence the option A is the incorrect option.
- B)The equation given in the problem is,
[tex]14x&=7(2x+2)[/tex]
Solve it further,
[tex]14x&=14x+14\\.\;\;\;0=14[/tex]
Thus this equation has no solution. Hence the option B is the incorrect option.
- C)The equation given in the problem is,
[tex]5x+3=-2(2x+3)[/tex]
Solve it further,
[tex]5x+3=-(4x+6)\\5x+3=-4x-6[/tex]
Bring the same variable terms one side.
[tex]5x+4x=-6-3\\9x=-9\\x=-1[/tex]
As the expression of equation gives the value of variable which is -1.Thus this equation has one solution.
Hence the option C is the correct option.
- D)The equation given in the problem is,
[tex]3(4x+2)-9=12x-3[/tex]
Solve it further,
[tex]12x+6-9=12x-3\\2x-3=12x-3\\.\;\;\;\;\;\;\;0=0[/tex]
Thus, this equation does not has one solution.
Hence the option D is the incorrect option.
Hence the equation which has only one solution are,
[tex]5x+3=-2(2x+3)[/tex]
Thus, the option C is the correct option.
Learn more about the solution of equation here;
https://brainly.com/question/21283540
