The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

Solve All Linear Equations.

When Does The Left Side Equal The Right Side?

      Yes, to solve means to find all numbers that make a statement true and to solve also means to undo each operation from lowest to highest to reveal the value of 1x. But solve has more than an computational meaning.

      To solve means to answer the question, "When does the left side equal the right side?"

      Usually we do the computation or manipulation and get an answer. Below, thought in addition to computation or manipulation is required. To solve these equations, ask, "When does the left side equal the right side?"

      These equations were chosen because they are not routine questions yet may be encountered when completing routine computation and manipulation of equations.

      When solving equations, one is focused on the selecting and executing the right step and not necessarily in the meaning of the problem. Often equations like those above come as a shock and create frustration because the above results are not expected.

      Review the following and go with confidence. If a result seems strange, think of its meaning and state the appropriate solution.

Solutions to Equations

Three kinds of solutions are possible when one solves a linear equation:

  • one solution
            - the statement is sometimes true, for example, x = 5 or 2 = y,
  • every number is a solution
            - the statement is always true, for example, 5 = 5 or x = x, or,
  • there is no solution
            - the statement is false, for example, 10 = 5 or 2 + 3 = 6 + 1.

      Try these on your own. Then check the work and solutions below.

Solve.     ex. 1.     2x + 2(x - 1) = 2
ex. 2.2x + 2(x - 1) = 4x +1
ex. 3.2x + 2(x - 1) = 4x - 2
ex. 4.3x + 4 = 2(x+2) + x

Solve an equation with 1 solution.

Solve an equations with no solution.

Solve an equation in which all numbers are solutions., Unit 24   © 2008, A. Azzolino