QUESTION

# Solve the following linear equation: $4z+3=6+2z$.

Hint: Take all the variable parts on the lhs of the equation and all the constant parts on the Right Hand Side of the equation.

Given equation : $4z+3=6+2z$

After performing the above steps, we get

$4z-2z=6-3$, then finally we will find the value of the variable in the equation.

It is given in the question that we have two linear equations $4z+3$ and $6+2z$, the value of linear equations are equal thus, they are equated with each other as $4z+3=6+2z$. Now, we have to find the value of the variable involved here, that is, z.

On transporting $2z$ from Right Side of the equation to Left Side, we get, $4z-2z+3=6$, on transporting 3 from Left Side to Right side we get, $4z-2z=6-3$. Solving further,

= $2z=3$

= $z=\dfrac{3}{2}$.

Thus, the value of variable, z, in the linear equation is $\dfrac{3}{2}$.

Note: This is a very basic linear equation question which can be solved directly but we have to keep in mind that we have to keep in mind that we may make mistakes in changing the sign while transporting from the left side of the equation to the right side of the equation. Therefore, we must keep both of our eyes while changing the sign of the terms in the equation. Also, After getting the value of z, we can substitute it in the given equation and check if it satisfies the given equation. Both the sides of the linear equation must be equal. Or both the linear equations on either side of the given equation must result in the same value, after substituting the value of z.