Solving for a Variable:

Solving Variables on Both Sides of the Equation

So far we’ve only seen equations with a single variable. There are equations that have variables in more than one place. For example, \(3{\text{x}} + 4 = {\text{x}}\). How do we solve these? The first video will explain some of the tools we will use, then the second video will show how to solve these kinds of equations.

Video Source (03:22 mins) | Transcript

Video Source (09:43 mins) | Transcript

Tools taught in the first video:

When faced with a problem, start by combining any like terms on the same side of the equation. Then combine like terms from both sides of the equation. After that, use the things we learned in last week’s lesson of adding or multiplying by the inverse as needed. Remember, we can add, subtract, multiply, or divide all we want, as long as we do it to both sides of the equation.

Additional Resources

Practice Problems

Solve for the following variables:

  1. \(2 - 7{\text{g}} = -9{\text{g}}\)

  2. \(12 + 3{\text{W}} = -4 + {\text{W}}\)

  3. \({\text{m}} {-} 3 = 2{\text{m}} - 3\)

  4. \(3 - 6{\text{P}} = -6 - 7{\text{P}}\)

  5. \(6{\text{x}} {-} 1 = -5 + 7{\text{x}}\)

  6. \(7 - 5{\text{C}} = -9 - 9{\text{C}}\)

Solutions

  1. \(-1\)

  2. \(-8\) (Written Solution)

  3. 0 (Solution Video | Transcript)

  4. \(-9\) (Written Solution)

  5. 4

  6. \(-4\) (Solution Video | Transcript)