Question

How do you solve $5m+2(m+1)=23$?

Answer 1

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

Complete step by step solution:
The given equation says that $5m+2(m+1)=23$.
Let us analyse the above equation and try to simplify the equation by performing some mathematical operations on both the sides.
We shall first open up the brackets since brackets have the first priority in mathematical operations.
When do this we get that equation as $5m+2m+2=23$ ….. (i)
Now, we can group all the multiples of m on anyone side of the equation (say left hand side) and the constant terms on the other side of the equation (right hand side). We can do this by subtracting 2 on both the sides of equation (i).
With this we get that $5m+2m+2-2=23-2$, which implies that
$5m+2m=21$
Now, we can add the terms that are multiples of m.
Then, we get that $7m=21$
In the above equation we can see that the number 7 is a factor of 21 (or 21 is a multiple of 7). Therefore, we shall divide both the sides of the equation by 7.
This will give us that $m=3$
Therefore, the solution of the given equation is $m=3$.

Note: Students must note that when we perform mathematical operations on an equation we must keep in mind the equation always holds true. That is why we perform the same operations on both sides. Students must also 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.