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How do you solve $2x=7x+10$ ?

Last updated date: 12th Jul 2024
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Hint: We are asked to find the solution of $2x=7x+10$
Firstly, we learn what linear equation is in 1 variable term. We use a hit and trial method to find the value of ‘x’ one by one by hitting arbitrary values and looking for needed values. Another method is to apply algebra. We subtract terms to get to our final term and get our required solution.

Complete step by step answer:
We are given that we have $2x=7x+10$ . We are asked to find the value of ‘x’, or we are asked how we will be able to solve this expression.
We learn about the equation on one variable. One variable simply represents the equation that has one variable (say x, y, or z) and another one constant.
For example:
$x+2=4,2-x=2,2x,2y$ etc
Our equation $x+3=5$ also has just one variable ‘x’.
We have to find the value of ‘x’ which will satisfy our given equation.
Firstly we try by the method of hit and trial. In which we will put a different value of ‘x’ and take which one fits the solution correctly.
Let $x=0$
We put $x=0$ in $2x=7x+10$ we get –
  & 2\times 0=7\times 0+10 \\
 & 0=10 \\
Which is not true so,
Now let us take $x=1$
We put $x=1$ in $2x=7x+10$ we get –
$2\times 1=7\times 1+10$
Again this is not true.
So, $x=1$ is also not a solution.
Let us take $x=-1$
We put $x=-1$ in $2x=7x+10$ we get –
  & 2\times \left( -1 \right)=7\times \left( -1 \right)+10 \\
 & -2=3 \\
Which is not true also
So, $x=-1$ is not a solution as well.
Now let us take $x=-2$
We put $x=-2$ in $2x=7x+10$ we get –
  & 2\left( -2 \right)=7\left( -2 \right)+10 \\
 & -4=-14+103 \\
 & -4=-4 \\
Which is true, so we get $x=-2$ as the solution of $2x=7x+10$ .
Another way to solve this is to use the algebraic operation. We will use multiplication, division, addition operation with variables and constants to simplify our problem and get our required solution.
We have –
Subtract ‘7x’ on both sides, we get –
By simplifying, we get –
$-5x=10$ (as $2x-7x=-5x$ and $7x-7x=0$ )
Now divide both sides by ‘-5’, we get –
$x=-2$ is the solution to this problem.

Remember that, we cannot add the variable to the constant. Usual mistakes like this where one adds constants with variables usually happen.
For example: $3x+6=9x$ , here one added ‘6’ with ‘3’ of x makes it ‘9x’, this is wrong, we cannot add constant and variable at once. Only the same variables are added to each other.
Method of hit and trial is not always useful because sometimes the solution lies in another direction and we may look for it on the other side so we largely depend on algebra.