Final answer:
To eliminate the factors in an equation, find the least common denominator of all fractions, then multiply each term by this number to remove the fractions and solve the equation.
Step-by-step explanation:
To eliminate the factors in the equation 1/2x - -5/4 + 2x = 5/6 + x, you can find the least common denominator (LCD) of the fractions involved, which is typically the product of the denominators after simplifying any common factors. Once the LCD is determined, you can multiply each term of the equation by this number, which will effectively eliminate the fractional parts and allow you to solve for the variable x.
Remember, when you multiply one side of an equation, you must multiply the entire other side as well to maintain equality. This means encasing sides with more than one term in brackets before performing the multiplication. For example, multiplying one side by 12 would require you to multiply each term by 12, resulting in an equation of the form (12 × 1/2x) - (12 × -5/4) + (12 × 2x) = (12 × 5/6) + (12 × x). Simplifying this will eliminate the fractions and make it easier to solve the equation.