Question

Construct $3$ equations starting with the solution:

$z=10$

Answer 1

We have, $z=10$

Multiply both sides by $3$

$$\begin{gathered} 3\times z=3\times 10 \\ \Rightarrow 3z=30 \end{gathered}$$

Adding $5$ on both sides

$$\begin{gathered} 3z+5=30+5 \\ \Rightarrow 3z+5=35 \end{gathered}$$

Again, for $z=10$

Multiplying both sides by $10$

$$\begin{gathered} 10\times z=10\times 10 \\ \Rightarrow 10z=100 \end{gathered}$$

Subtracting $3$ from both sides

$$\begin{gathered} 10z-3=100-3 \\ \Rightarrow 10z-3=97 \end{gathered}$$

Again, for $z=10$

Dividing both sides by $5$

$$\begin{gathered} \frac{z}{5}=\frac{10}{5} \\ \Rightarrow \frac{z}{5}=2 \end{gathered}$$

Hence, the $3$ equations can be: $3z+5=35$, $10z-3=97$ and $\frac{z}{5}=2$.