This equation means that if you begin with some unknown number, [latex]x[/latex], and subtract [latex]6[/latex], you will end up with [latex]8[/latex]. You are trying to figure out the value of the variable [latex]x[/latex].

Using the Addition Property of Equality, add [latex]6[/latex] to both sides of the equation to isolate the variable. You choose to add [latex]6[/latex] because [latex]6[/latex] is being subtracted from the variable.

[latex]\displaystyle \begin{array}{r}x-6\,\,\,=\,\,\,\,8\\\,\,\,\,\,\,\,\underline{+\,6\,\,\,\,\,\,\,\,+6}\\\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,=\, 14\end{array}[/latex]

[latex]x+10=-65[/latex]

Since [latex]10[/latex] is being added to the variable, subtract [latex]10[/latex] from both sides. Note that subtracting [latex]10[/latex] is the same as adding [latex]–10[/latex].

[latex]\displaystyle \begin{array}{r}x+10\,\,=\,\,\,\,-65\\\,\,\,\,\,\underline{-10\,\,\,\,\,\,\,\,\,\,-10}\\\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,=\,\,\,-75\end{array}[/latex]

To check, substitute the solution, [latex]–75[/latex] for [latex]x[/latex] in the original equation, then simplify.

[latex]\displaystyle \begin{array}{r}\,\,\,\,\,x+10\,\,\,=-65\\-75+\,10\,\,\,=-65\\\,\,\,\,\,\,\,\,\,\,\,-65\,\,\,=-65\end{array}[/latex]

This equation is true, so the solution is correct.