Exercise 15 Page 254

We are given an equation. x+5=16 We want to know why we subtract 5 from both sides of the equation when solving it. To explain why, we will first review the Subtraction Property of Equality and the Addition Property of Equality.

From the Addition and Subtraction Properties of Equality, we can conclude that adding the same number to both sides of an equation or subtracting the same number from both sides of an equation results in an equivalent equation. Now let's look at some examples.

In light of this information, let's get back to our exercise. Notice that the left side of the equation has two terms that are being added together. x + 5=16 We undo addition using subtraction because addition and subtraction are inverse operations. Therefore, we need to subtract 5 from the left-hand side. To maintain equality on both sides of the equation, we need to subtract 5 from the right-hand side as well. x+5= 16 -5 -5 x = 11 The solution of the equation is x=11.

Checking Our Answer

Checking the Answer

We can substitute the value of x into the equation to check our answer.

x+5=16

Substitute

x= 11

{\color{#0000FF}{11}}+5\stackrel{?}=16

AddTerms

Add terms

16=16 ✓

Both sides of the equation are equal, so the value of x that we found is correct.