Question

Construct $3$ equations starting with the solution:

$x=-5$

Answer 1

We have, $x=-5$

Multiply both sides by $3$

$$\begin{gathered} 3\times x=3\times -5 \\ \Rightarrow 3x=-15 \end{gathered}$$

Adding $5$ on both sides

$$\begin{gathered} 3x+5=-15+5 \\ \Rightarrow 3x+5=-10 \end{gathered}$$

Again, for $x=-5$

Multiplying both sides by $10$

$$\begin{gathered} 10\times x=10\times -5 \\ \Rightarrow 10x=-50 \end{gathered}$$

Subtracting $3$ from both sides

$$\begin{gathered} 10x-3=-50-3 \\ \Rightarrow 10x-3=-53 \end{gathered}$$

Again, for $x=-5$

Dividing both sides by $5$

$$\begin{gathered} \frac{x}{5}=\frac{-5}{5} \\ \Rightarrow \frac{x}{5}=-1 \end{gathered}$$

Hence, the $3$ equations can be: $3x+5=-10$, $10x-3=-53$ and $\frac{x}{5}=-1$.