The prime use for simple equations is in instilling the fundamentals of algebra. A simple equation such as 5(x ' 3) ' 7(6 ' x) = 24 ' 3(8 ' x) ' 3 provides a basic exercise in order of operations and combining like terms, the distributive property of multiplication with its 5, -7, and 21 next to parentheses, and balancing equations by doing the same operation to each side.
Once simple equations are mastered, the student can move on to binomials, polynomials, quadratics and all higher forms of math. If a student knows how to solve for single variables, he has everything he needs to solve complex equations with multiple variables such as polynomials, and is further equipped to handle complex formulas such as the quadratic equation. Knowing how to perform such equations is crucial not only in math, but has wide applications in computer programming and physics, such as when calculating forces.
Graphing simple equations is often the student's first introduction to graphing from an equation rather than an x and y coordinate chart. Simple equations teach the basic properties of functions, how to use graphs to find solutions for equations and what to expect for the basic shape of graphs: that the graph of 5x is linear, 5x^2 is a parabola and 5x^3 is a hyperbola, the properties of these shapes, and what they mean.
Teaching students abstract math is really teaching them how to think. Simple equations puzzles help students learn to plan several steps ahead and develop methodological problem-solving strategies. They also train students to follow directions, since if one rule is skipped, misunderstood or forgotten, the whole problem is wrong. Such intricacies also encourage students to be meticulous, work slowly, check their work and learn patience.