Question

How do you solve $5(x-2)+x=6(x-4)$?

Answer 1

Hint: The equation given in the above question is a linear equation in one variable, that is x. The question says that we have to solve the given equation in x. In other words, we have to find the values of x which will satisfy the given equation. Try to find the value of x by performing some mathematical operations.

Complete step by step solution:
The equation in the given question says that $5(x-2)+x=6(x-4)$.
Let the analyse the above equation and try to find the value of x for which the equation is valid or it holds true. Let us begin to simplify the equation by opening up the brackets on both the sides of the equation.
When open up the brackets (multiply the multiple outside the bracket to each of the elements inside the bracket), we get that
$5x-10+x=6x-24$
Now, we can club the multiples of x on one side of the equation (say left hand side) and club the constant terms on the other side (right hand side) of the equation.
With this we get that equation as $5x-6x+x=-24+10$
If we simplify further we get that the left hand side of the equation becomes $5x-6x+x=0$ and the right hand becomes -14.
But we know that the numbers 10 and -14 are not equal.
Therefore, the given equation is invalid.

Note: There are many ways in which we can solve this question. We can also add or subtract some terms such that you get all x terms on one side and the constant terms in the other. However, students must note that the number of solutions to a given equation in one variable is always less than or equal to the degree of the polynomial in the given equation.