To solve the equation [tex]\(\left(-\frac{1}{4}\right)x = 6\)[/tex] for [tex]\(x\)[/tex], we will follow these steps:
1. Isolate the variable [tex]\(x\)[/tex]:
The equation is [tex]\(\left(-\frac{1}{4}\right)x = 6\)[/tex]. To isolate [tex]\(x\)[/tex], we need to eliminate the coefficient [tex]\(\left(-\frac{1}{4}\right)\)[/tex]. This can be done by multiplying both sides of the equation by the reciprocal of [tex]\(-\frac{1}{4}\)[/tex], which is [tex]\(-4\)[/tex].
[tex]\[
\left(-\frac{1}{4}\right)x \cdot (-4) = 6 \cdot (-4)
\][/tex]
2. Simplify the equation:
On the left-hand side, [tex]\(\left(-\frac{1}{4} \cdot -4\right)x\)[/tex] simplifies to [tex]\(1x\)[/tex] or just [tex]\(x\)[/tex]. On the right-hand side, [tex]\(6 \cdot (-4)\)[/tex] simplifies to [tex]\(-24\)[/tex].
[tex]\[
x = -24
\][/tex]
3. Check possible answers:
The possible answers provided are:
- [tex]\(x = -1 \frac{1}{2} \)[/tex] or [tex]\(-1.5\)[/tex]
- [tex]\(x = 24\)[/tex]
- [tex]\(x = 6 \frac{1}{4}\)[/tex] or [tex]\(6.25\)[/tex]
- [tex]\(x = -24\)[/tex]
From our solution, [tex]\(x = -24\)[/tex] is the correct answer.
Therefore, the solution to the equation [tex]\(\left(-\frac{1}{4}\right)x = 6\)[/tex] is:
[tex]\[
x = -24
\][/tex]
