Solve for [tex][tex]$x$[/tex]:[/tex]

[tex]\left(-\frac{1}{4}\right) x = 6[/tex]

A. [tex]x = -1 \frac{1}{2}[/tex]
B. [tex]x = 24[/tex]
C. [tex]x = 6 \frac{1}{4}[/tex]
D. [tex]x = -24[/tex]



Answer :

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]