We want to verify if any values contained in the replacement set are solutions of this equation. We will replace the variable with each value from the set and check if the equation is true for any of them.

$w$	$9 + w = 17$	Simplify	True or False?
$7$	$9 + 7 = ? 17$	$16 \neq = 17$	False
$8$	$9 + 8 = ? 17$	$17 = 17$	True
$9$	$9 + 9 = ? 17$	$18 \neq = 17$	False

The equation is true when

w = 8 .

Therefore, the solution is

8 .

Alternative Solution

Using the Properties of Equality

In later chapters, you will learn more about solving equations using the four main Properties of Equality.

Properties of Equality
Property	Rule
Addition Property of Equality	If $a = b,$ then $a + c = b + c .$
Subtraction Property of Equality	If $a = b,$ then $a - c = b - c .$
Multiplication Property of Equality	If $a = b,$ then $a \times c = b \times c .$
Division Property of Equality	If $a = b$ and $c \neq = 0,$ then $\frac{a}{c} = \frac{b}{c} .$

These properties tell us how we can change an equation while making sure that the left-hand side and the right-hand side are still equal to each other. Anything we do to the left-hand side, we also need to do to the right-hand side. Let's see how we would solve the given equation!

9 + w = 17

SubEqn

$LHS - 9 = RHS - 9$

9 + w - 9 = 17 - 9

SubTerm

Subtract term

w = 8

When we solved the equation using the Properties of Equality, we got the same answer as the one we found from the replacement set!

Exercise