Because of the Addition and Subtraction Properties of Equality, we know that adding the same number to both sides of an equation or subtracting the same number from both sides results in an equivalent equation. Now let's look at some examples.
When we solve an equation for x, we want the left-hand side of the equation to only have x-terms and the right-side of the equation to only have numbers.
x-terms=numbers
We can usually do this by using inverse operations. Addition and subtraction are inverse operations — we undo addition using subtraction and we undo subtraction using addition. However, for our equation, notice that 6 and 2x are both added to both sides of the equation.
x+ 6+ 2x= 2x+ 6+4
⇓
x=4
Instead of directly applying the Properties of Equality, we can use what we know about the Addition Property of Equality to cancel out these terms. We know that because they are added to both sides of the equation, they do not change the value of x.
x+6+2x=2x+6+4
⇓
x=4
This means that x is 4.
Checking Our Answer
Checking Our Answer
We will also solve this equation algebraically. We will subtract 6+2x from both sides of the equation using the Subtraction Property of Equality.
