Sections 1. 1 and 1. 2: linear equations and application. When solving a linear equation, we are looking for all values of x that when substituted back into the original equation yield a true statement. The goal is to find the values that satisfy the original equation regardless of the method. Step one is to find a common denominator 20. One way to find a denominator is to multiply all the denominators together. 40 and 80 are both common denominators, but we are looking for the lcd (least common denominator) which is 20. To find lcd look at all of the denominators and their prime factorizations. All of the primes to their highest powers without repeating numbers (all of the primes to the largest power to which they appear on the list of denominators). Multiply the entire equation by the lcd in order to get rid of the fractions in the problem.