Question
The equation among the following that have infinitely many solutions is
- 2x = x +5
- 2x + 5 = 5x + 2
- 3x + 7 = 3x + 7
- 2x = 5x
Hint:
An equation contains constants, variables and an equal sign. It has two sides called LHS and RHS. A linear equation in one variable is an equation with only one variable and the highest power of the variable should be one. Here, we have to find the linear equation in one variable with infinitely many solutions which can be done determining whether the variables and constants on both sides of the equation is equal or not.
The correct answer is: 3x + 7 = 3x + 7
Here, we have to find the equation which has infinitely many solutions.
In option a the equation is 2x=x+5.
Here, the variable and constant terms are different so, it doesn't have infinitely many solutions. Similarly, in option b the equation is 2x+5=5x+2.
Here, the variable and constant terms are different so, it doesn't have infinitely many solutions.
In option c the equation is 3x+7= 3x+7.
Here, the variable and constant terms are same on both sides of the equation, which on solving will give 0=0. So, this equation has infinitely many solutions.
In option d the equation is 2x=5x.
Here, the variable and constant terms are different so, it doesn't have infinitely many solutions.
So, the equation having infinitely many solutions is 3x+7= 3x+7.
Therefore, the correct option is c,i.e., 3x+7=3x+7.
The linear equations with one variable is an equation which has only one variable and the highest power of the variable should be one. The linear equations in one variable having infinitely many solutions have same variable and constant terms on both the sides of the equation. On solving the equation they will get cancelled and will give 0=0 as result.
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