To solve the following linear equation, we multiply each...

To solve the following linear equation, we multiply each side by the least common denominator of all the fractions in the equation. What is this $\mathrm{LCD} ?$
$$
\frac{3}{4} x-\frac{1}{3} x=\frac{5}{6} x-5
$$

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Key Concepts

Fractions

Fractions represent a part of a whole and are written as one number (the numerator) divided by another number (the denominator). When fractions are involved in equations, special techniques are needed to combine or eliminate them to simplify the solving process.

Clearing Fractions Technique

Clearing fractions involves multiplying every term in an equation by the least common denominator of all the fractions present. This process eliminates the denominators, transforming the equation into one with whole numbers, which simplifies further manipulation and solution.

Linear Equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. It typically involves finding the value of the variable that satisfies the equality, and solving these equations is a fundamental part of algebra.

Least Common Denominator (LCD)

The least common denominator is the smallest number that is a multiple of the denominators of all the fractions in an equation. It is used to rewrite fractions so that they have a common denominator, making it easier to add, subtract, or clear the fractions from the equation.

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