Answer:
B) [tex]x=-\frac{8}{27}[/tex]
Step-by-step explanation:
[tex]-\frac{8}{9}=-\frac{2}{3}x(-4\frac{1}{2})[/tex]
- To start things off, lets convert any mixed numbers like [tex]-4\frac{1}{2}[/tex] into improper fractions. In this case [tex]-4\frac{1}{2}[/tex] as an improper fraction is [tex]-\frac{9}{2}[/tex].
[tex]-\frac{8}{9}=-\frac{2}{3}x(-\frac{9}{2})[/tex]
- Now let's multiply [tex]-\frac{2}{3}x[/tex] by [tex]-\frac{9}{2}[/tex]. When multiplying fractions, all you need to do is multiply the numerators and denominators separately. Your final answer should be [tex]\frac{18}{6}x[/tex].
- *Note: a negative times a negative is a positive, so that's why we now have an even number in front of [tex]x[/tex] instead of a negative number.
[tex]-\frac{8}{9}=\frac{18}{6}x[/tex]
- Now we want to isolate [tex]x[/tex], so we'll have to divide [tex]-\frac{8}{9}[/tex] by [tex]\frac{18}{6}[/tex], but dividing these two fractions seems like a pain. To make things a bit easier, let's turn our improper fraction into a whole number. To change this improper fraction into a whole number, we should ask ourselves what times [tex]6[/tex] is equal to [tex]18[/tex]? In this case, the answer is 3, so [tex]\frac{18}{6}[/tex] is actually the same thing as the whole number [tex]3[/tex].
- *Note: In general, keeping fractions as either improper fractions or whole numbers will make doing math easier. Avoid mixed numbers like [tex]-4\frac{1}{2}[/tex] when trying to do math and simply change improper fractions into mixed numbers once you have your final solution.
[tex]-\frac{8}{9}=3x[/tex]
- Now divide [tex]-\frac{8}{9}[/tex] by [tex]3[/tex]. Think of it as multiplying the denominator of [tex]-\frac{8}{9}[/tex] by [tex]3[/tex].
[tex]-\frac{8}{27}=x[/tex]
