the ratio of -15 (of the area term) and +5 (of the length term) suggests a term for the width ending in -3. and we need an x in there to get x² for the area.
Just as multiplying two by twelve is faster than counting to 24 or adding 2 twelve times, algebra helps us solve problems more quickly and easily than we could otherwise. Algebra also opens up whole new areas of life problems, such as graphing curves that cannot be solved with only foundational math skills.
