To solve for [tex]\( w \)[/tex] in the equation [tex]\( -9 = \frac{2}{w} \)[/tex], follow these step-by-step instructions:
1. Start with the given equation:
[tex]\[
-9 = \frac{2}{w}
\][/tex]
2. To eliminate the fraction, multiply both sides of the equation by [tex]\( w \)[/tex]:
[tex]\[
-9w = 2
\][/tex]
3. Next, solve for [tex]\( w \)[/tex] by isolating [tex]\( w \)[/tex]. Divide both sides of the equation by [tex]\(-9\)[/tex]:
[tex]\[
w = \frac{2}{-9}
\][/tex]
4. Simplify the fraction, if possible. In this case, [tex]\(\frac{2}{-9}\)[/tex] is already in its simplest form:
[tex]\[
w = -\frac{2}{9}
\][/tex]
Thus, the solution to the equation [tex]\(-9 = \frac{2}{w}\)[/tex] is:
[tex]\[
w = -\frac{2}{9}
\][/tex]
Alternatively, in decimal form, the value of [tex]\( w \)[/tex] is approximately:
[tex]\[
w = -0.2222222222222222
\][/tex]
