Solving an Equation Algebraically When the Variable Appears on Both Sides

Solve the following equation: $4 (x −3) + 12 = 15 −5 (x + 6) .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Apply standard algebraic properties.

$\begin{matrix} 4 (x - 3) + 12 & = & 15 - 5 (x + 6) \\ 4 x - 12 + 12 & = & 15 - 5 x - 30 & Apply the distributive property . \\ 4 x & = & −15 - 5 x & Combine like terms . \\ 9 x & = & −15 & Place x -terms on one side and simplify . \\ x & = & - \frac{15}{9} & Multiply both sides by \frac{1}{9}, the reciprocal of 9 . \\ x & = & - \frac{5}{3} \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the equation in one variable: $−2 (3 x - 1) + x = 14 - x .$

How did it go?