Question

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

Short answer

On verifying the equation by putting the value of $z=\frac{1}{2}$ the equation is satisfied.

Step-by-step solution

Step-1 – Apply the concept of solving the equations

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.

Step-2 – Solve the equation using above concept 

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

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

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

Step-3 – Verify or Check the solution

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.