Solve the equation $2z-3=-6z+1$and verify the equation.

We have $4$ways of solving one-step equations: Adding, Subtracting, multiplication and division.

If we add the same number to both sides of an equation, both sides will remain equal.

If we subtract the same number from both sides of an equation, both sides will remain equal.

If we divide both sides of an equation by the same number, both sides will remain equal.

If we multiply both sides of an equation by the same number, both sides will remain equal.

$2z-3=-6z+1$

On Adding $6z+3$on both sides of the equation as

$\begin{array}{l}2z-3=-6z+1\\ 2z-3+6z+3=-6z+1+6z+3\\ 8z=4\end{array}$

Now dividing the equation by $4$we get

$\begin{array}{l}\frac{8z}{4}=\frac{4}{4}\\ z=\frac{1}{2}\end{array}$

On verifying the equation by putting the value of $z=\frac{1}{2}$in the equation as

$\begin{array}{l}2\left(\frac{1}{2}\right)-3=-6\left(\frac{1}{2}\right)+1\\ 1-3=-3+1\\ -2=-2\end{array}$

Therefore, it is proved and $z=\frac{1}{2}$ is solution of the given equation.