To solve the equation [tex]\(\frac{5}{4} = -12\)[/tex], we first need to clarify the question since as it stands, [tex]\(\frac{5}{4}\)[/tex] is a fraction and cannot equal [tex]\(-12\)[/tex]. It's likely the equation should be [tex]\(\frac{5}{x} = -12\)[/tex]. So, let's solve for [tex]\(x\)[/tex] under this assumption:
1. Let's start with the equation:
[tex]\[
\frac{5}{x} = -12
\][/tex]
2. To isolate [tex]\(x\)[/tex], we can multiply both sides of the equation by [tex]\(x\)[/tex]:
[tex]\[
5 = -12x
\][/tex]
3. Next, we solve for [tex]\(x\)[/tex] by dividing both sides of the equation by [tex]\(-12\)[/tex]:
[tex]\[
x = \frac{5}{-12}
\][/tex]
4. Simplifying [tex]\(\frac{5}{-12}\)[/tex] gives us:
[tex]\[
x = -0.4166666666666667
\][/tex]
Now, we need to examine the given options to find the closest match to our calculated value of [tex]\(x = -0.4166666666666667\)[/tex]:
- Option A: [tex]\(x=-3\)[/tex]
- Option B: [tex]\(x=-48\)[/tex]
- Option C: [tex]\(x=48\)[/tex]
- Option D: [tex]\(x=3\)[/tex]
Comparing [tex]\(-0.4166666666666667\)[/tex] with the provided options, we see that it is closest to the value [tex]\(-3\)[/tex] in Option A.
Therefore, the solution to the equation [tex]\(\frac{5}{x} = -12\)[/tex] is:
A. [tex]\(x = -3\)[/tex]
