Question
Teacher asked students the number of solutions of 25(x + 1) = 5(5x + 2) +15, the answers the students responded are
Katty: The solution is x = 2
Katherine: The equation has no solution
Steve: The equation has infinitely many solutions
- Katty is correct
- Katherine is correct
- Steve is correct
- All three failed to give the correct answer
Hint:
An equation has a constant, variable and an equal to sign. It has two sides LHS and RHS. A linear equation in one variable is equation with only one variable and in which the highest degree is 1. Here, we have to find the value of unknown value, by operating both sides with the same number so that the equation will be balanced.
The correct answer is: Steve is correct
In the question the given equation is 25(x + 1) = 5(5x + 2) +15.
We have to find the value of x.
Step 1: Solve the brackets on both sides.
25(x + 1) = 5(5x + 2) +15
25x+25= 25x+10+15
25x+25x= 25x+25
Here, the variable and constant terms are same on both sides, which on solving will give 0=0. So, this equation has infinitely many solutions.
Therefore, the correct option is c, i.e., Steve is correct.
The linear equations with one variable are 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 if it has 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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