We can solve for

w

using the various Properties of Equality. Whatever is done to the left-hand side must also be done to the right-hand side. Doing so keeps both sides of the equation equal to one another and allow the variable to be isolated to solve the equation.

17 = \frac{4 5}{w} + 2

SubEqn

$LHS - 2 = RHS - 2$

15 = \frac{4 5}{w}

MultEqn

$LHS \cdot w = RHS \cdot w$

15 w = 45

DivEqn

$LHS / 15 = RHS / 15$

w = 3

Alternative Solution

Using the Guess and Check Method

To solve the equation, we need to find out for what value(s) of

w

the equation will remain equal. We can see that both sides of the equation have been simplified as much as possible. We should start by rewriting the equation so the both sides look more similar to each other.

17 = \frac{4 5}{w} + 2 \Leftrightarrow 15 + 2 = \frac{4 5}{w} + 2

Looking at the equation this way, we can see that

15

is equal to

45

divided by

w .

For what value(s) of

w

is this true? Let's find out with a table of values. This method is called the guess and check method.

$w$	$15 = \frac{4 5}{w}$	Simplify	True or False?
$1$	$15 = ? \frac{4 5}{1}$	$15 \neq = 45$	False
$2$	$15 = ? \frac{4 5}{2}$	$15 \neq = \frac{4 5}{2}$	False
$3$	$15 = ? \frac{4 5}{3}$	$15 = 15$	True

The solution to the equation is $w = 3 .$

Exercise 49 Page 46

Hints

Check the answer

Practice exercises

Asses your skill

Alternative Solution