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Any algebraic equation without exponents or roots is known as a linear equation.
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!
Multiply by the Reciprocal! – The easiest way to rid a variable of a fractional co-efficient is to multiply both sides of the equation by the reciprocal of the co-efficient.
If your variable has two fractional co-efficients, multiply both sides of the equation by both reciprocals.
- – 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, cross-multiplication 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!