Using Subtraction Property of Equality

Solving Equations Using the Subtraction Property of Equality

Our puzzle has given us an idea of what we need to do to solve an equation. The goal is to isolate the variable by itself on one side of the equations. In the previous examples, we used the Subtraction Property of Equality, which states that when we subtract the same quantity from both sides of an equation, we still have equality.

Think about twin brothers Andy and Bobby. They are \(17\) years old. How old was Andy \(3\) years ago? He was \(3\) years less than \(17,\) so his age was \(17-3,\) or \(14.\) What about Bobby’s age \(3\) years ago? Of course, he was \(14\) also. Their ages are equal now, and subtracting the same quantity from both of them resulted in equal ages \(3\) years ago.

\(\begin{array}{c}a=b\\ a-3=b-3\end{array}\)

Example

Solve: \(x+8=17.\)

Solution

We will use the Subtraction Property of Equality to isolate \(x.\)

Subtract 8 from both sides.
Simplify.

Since \(x=9\) makes \(x+8=17\) a true statement, we know \(9\) is the solution to the equation.

Example

Solve: \(100=y+74.\)

Solution

To solve an equation, we must always isolate the variable—it doesn’t matter which side it is on. To isolate \(y,\) we will subtract \(74\) from both sides.

Subtract 74 from both sides.
Simplify.
Substitute \(26\) for \(y\) to check.

Since \(y=26\) makes \(100=y+74\) a true statement, we have found the solution to this equation.