Could any of y'all help me?

1 answer:

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Law Incorporation [45]

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B) $x=-\frac{8}{27}$

Step-by-step explanation:

$-\frac{8}{9}=-\frac{2}{3}x(-4\frac{1}{2})$

To start things off, lets convert any mixed numbers like $-4\frac{1}{2}$ into improper fractions. In this case $-4\frac{1}{2}$ as an improper fraction is $-\frac{9}{2}$ .

$-\frac{8}{9}=-\frac{2}{3}x(-\frac{9}{2})$

Now let's multiply $-\frac{2}{3}x$ by $-\frac{9}{2}$ . When multiplying fractions, all you need to do is multiply the numerators and denominators separately. Your final answer should be $\frac{18}{6}x$ .
*Note: a negative times a negative is a positive, so that's why we now have an even number in front of $x$ instead of a negative number.

$-\frac{8}{9}=\frac{18}{6}x$

Now we want to isolate $x$ , so we'll have to divide $-\frac{8}{9}$ by $\frac{18}{6}$ , 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 $6$ is equal to $18$ ? In this case, the answer is 3, so $\frac{18}{6}$ is actually the same thing as the whole number $3$ .
*Note: In general, keeping fractions as either improper fractions or whole numbers will make doing math easier. Avoid mixed numbers like $-4\frac{1}{2}$ when trying to do math and simply change improper fractions into mixed numbers once you have your final solution.