Question

The difference between an integer $x$ and $-9$ is $6$. Find all possible values of $x$.

Answer 1

Step 1. Subtract $-9$ from $x$.

The expression of the difference of $x$ and $-9$ is $x-\left(-9\right)$.

The difference is $6$.

So, $x-\left(-9\right)=6$.

Solve the equation:

$\begin{array}{rcl}x-\left(-9\right)& =& 6\\ & \Rightarrow & x+9=6\\ & \Rightarrow & x=6-9\\ & \Rightarrow & x=-3\end{array}$

So, the unknown number is $-3$.

Step 2. Subtract $x$ from $-9$.

The expression of the difference of $x$ and $-9$ is $\left(-9\right)-x$.

The difference is $6$.

So, $-9-x=6$.

Solve the equation:

$\begin{array}{rcl}-9-x& =& 6\\ & \Rightarrow & -x=6+9\\ & \Rightarrow & -x=15\\ & \Rightarrow & x=-15\end{array}$

So, the unknown number is $-15$.

Thus, the two possible values of $x$ are $-3$ and $-15$.