Verifying a Solution of An Equation
Introduction
The rocks in this formation must remain perfectly balanced around the center for the formation to hold its shape.
If we carefully placed more rocks of equal weight on both sides of this formation, it would still balance. Similarly, the expressions in an equation remain balanced when we add the same quantity to both sides of the equation. In this tutorial, we will solve equations, remembering that what we do to one side of the equation, we must also do to the other side.
Verifying a Solution of an Equation
Solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same – so that we end up with a true statement. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle!
Solution of an equation
A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.
- Substitute the number in for the variable in the equation.
- Simplify the expressions on both sides of the equation.
- Determine whether the resulting equation is true (the left side is equal to the right side)
- If it is true, the number is a solution.
- If it is not true, the number is not a solution.
Example
Determine whether \(x=\frac{3}{2}\) is a solution of \(4x-2=2x+1\).
Solution
Since a solution to an equation is a value of the variable that makes the equation true, begin by substituting the value of the solution for the variable.
| Multiply. | |
| Subtract. |
Since \(x=\frac{3}{2}\) results in a true equation (4 is in fact equal to 4), \(\frac{3}{2}\) is a solution to the equation \(4x-2=2x+1\).
This lesson is part of:
Solving Linear Equations II