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Linear Equations
Any algebraic equation without exponents or roots is known as a linear equation.

Linear Equations
When isolating a variable, always work in the following order:
 1. Combine terms with the same variable through addition or subtraction.
 2. Add or subtract away numbers not directly attached to the variable.
 3. Multiply or divide out numbers directly attached to the variable.

Fractions: the “Denominator Trick”
To simplify an equation that contains a fraction, multiply the equation by the denominator of that fraction! Upon distribution, the denominator of your fraction will cancel out! • In most instances, this technique is considerably faster than converting each term in your equation to a common denominator.
**If your equation contains multiple denominators, multiply the equation by the lowest common denominator (LCD) of those denominators!

Fractional CoEfficients:
Multiply by the Reciprocal! – The easiest way to rid a variable of a fractional coefficient is to multiply both sides of the equation by the reciprocal of the coefficient.
If your variable has two fractional coefficients, multiply both sides of the equation by both reciprocals.

CrossMultiplication
 – An equation of two fractions can be simplified by multiplying the numerator of each fraction with the denominator of the other.
 8/3 = 2/p = 8p=6
 However, crossmultiplication CANNOT be performed if either side of the equation contains something in addition to a fraction! Such equations are best solved with the “denominator trick”.
8/3 = 2/p + 2

Equations With Multiple Variables: Isolating Combinations –
Some questions that involve linear equations ask you to solve for a combination of variables or terms such as “a – b” or “2x + y”.•

Such questions should be solved by isolating the combination. Do not attempt to solve each variable individually! In most instances, a single equation with multiple variables does not provide enough information to determine the value of any single variable.

Evaluations: Plug ‘n Chug –
Any question that supplies a question and a value that can be plugged into that question is commonly known an evaluation.• To solve such problems, simply plug the supplied value into the question!

