When dealing with Algebraic equations, you must deal with known and unknown quantities. These unknown quantities are called variables and are represented by symbols or letters, such as (*x*).

You can think of equations as one or more actions that result in a specific value. It can be as simple as 1 + 1 = 2 or include more complicated operations. If you recall, there is always an equal sign between the action and the result, which is a statement that one expression is equal to the other. Since algebraic expressions can have multiple parts, we can manipulate an equation to make several mathematical statements.

Generally this means having a single variable on one side of the equation with everything else on the other side. Think of it in terms of a balanced seesaw where a person on one end of the seesaw weighs exactly the same as the person on the other end of the seesaw. If one person is handed a 10‐lb. weight, the balance is broken; however, the balance can be restored if the other person is handed a 10‐lb. weight. The same is true if we remove the 10‐lb. weight from one person and not the other. Long story short, whatever is done to one side of the equation must be done to the other side of the equation to maintain equivalence or balance.

Often when balancing algebraic equations, you should pay attention to the number attached to the variable, called the coefficient (ex. For 9x, 9 is the coefficient). If no coefficient is present, then the coefficient is 1. If there is simply a negative sign (-*x*), the coefficient is -1.

**Example**

This is the method for balancing an equation. It is simply a matter of doing the opposite operation to “shift” parts of the equation to the other side. That is, if there is addition on one side, you can subtract that amount from both sides to move it to the other side. Take a look at a second example:

- What value of
*x*satisfies the equation*x*+ 5 = 5 ? - What value of
*x*satisfies the equation*x*- 9 = 4 ? - What value of
*x*satisfies the equation 2*x*= 18 ? - What value of
*x*satisfies the equation 4*x*+ 7 = 35 ? - What value of
*x*satisfies the equation 3*x*+ 1 =*x*+ 7 ?

**Answers to Practice Problems**

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