Verify 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.

How To

To determine whether a number is a solution to an equation.

Step 1. Substitute the number in for the variable in the equation.

Step 2. Simplify the expressions on both sides of the equation.

Step 3.  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 2.1

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.

\(4x-2=2x+1\)
Substitute \(\frac{3}{2}\) for \(x\)
 \( 4(\frac{3}{2}) - 2 \stackrel ? = 2(\frac{3}{2})+1 \)
Multiply. \( 6 - 2 \stackrel ? = 3+1\)
Subtract. \(4 = 4\) ✓

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 \(4x−2=2x+1\).

Try It 2.1

Is \(y=\frac{4}{3}\) a solution of \(9y+2=6y+3\)?

Try It 2.2

Is \(y=\frac{7}{5}\) a solution of \(5y+3=10y−4\)?

Back to '2.2: Addition/Subtraction Property of Equations'