Question

Explain why the equation 5z + 2 = 5z has no solution.

Short answer

The equation $5z+2=5z$has no solution because if we cancel 5z from both sides then we get 2 = 0, which is not true.

Step-by-step solution

Step-1 – Given

The given equation is $5z+2=5z$.

Step-2 – To determine

We have to find the reason why the equation $5z+2=5z$ has no solution.

Step-3 – Calculation

We try to solve the given equation for z, if possible

$\begin{array}{l}5z+2=5z\text{[Theoriginalequation.]}\\ 5z+2-5z=5z-5z\text{[Subtract5}z\text{fromeachside.]}\\ 2=0\text{[Simplify.]}\end{array}$

The statement $2=0$is false, so the equation has no solution.