# Solve for w . Simplify?

Feb 18, 2018

The value of $w$ is $- 24$.

#### Explanation:

As long as you perform the same operations on both sides of the equation, you can do whatever you want. First, multiply both sides by $8$, then, divide both sides by $- 5$.

$- \frac{5}{8} w = 15$

$- \frac{5}{8} w \cdot 8 = 15 \cdot 8$

$- \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}} w \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} = 15 \cdot 8$

$- 5 w = 15 \cdot 8$

$- 5 w = 120$

$w = \frac{120}{- 5}$

$w = - 24$

Feb 18, 2018

$w = - 24$

#### Explanation:

Step 1
The first priority is to isolate the variable $w$. To do this, we must divide both sides by $- \frac{5}{8}$.
$\frac{- \frac{5}{8} w}{- \frac{5}{8}} = \frac{15}{- \frac{5}{8}}$

Step 2
In order to simplify the left side of the equation, we can simply cancel the $- \frac{5}{8}$.
$w = \frac{15}{- \frac{5}{8}}$

Step 3
Now, we must simplify the right side of the equation. When dividing by a fraction, we can simply multiply by the fraction's reciprocal.
$w = 15 \cdot \left(- \frac{8}{5}\right)$

Step 4
We simplify.
$w = - 24$

Feb 18, 2018

$w = - 24$

#### Explanation:

$- \frac{5}{8} w = 15$    Solve for $w$

1) Clear the fraction by multiplying both sides by $8$ and letting the denominator cancel
$- 5 w = 120$

2) Divide both sides by $- 5$ to isolate $w$
$w = - 24$

$w = - 24$

Feb 18, 2018

$w = - 24$

#### Explanation:

We have:
$- \frac{5}{8} \cdot w = 15$

Using the fact that $\frac{a}{b} \cdot c = \frac{a c}{b}$, we can say that:

$- \frac{5}{8} \cdot \frac{w}{1} = \frac{15}{1}$

=>$- \frac{5 w}{8} = \frac{15}{1}$

Now, remember that:

If $\frac{a}{b} = \frac{c}{d}$, then:

$a d = c b$ where $b \ne 0$ and $d \ne 0$

=>$- \frac{5 w}{8} = \frac{15}{1}$

=>$\frac{- 5 w}{8} = \frac{15}{1}$

=>$- 5 w = 120$ Divide both sides by -5.

=>$w = - 24$