To solve the equation [tex]\( -\frac{3}{4} = \frac{x}{24} \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Understand the equation: The equation is given as [tex]\( -\frac{3}{4} = \frac{x}{24} \)[/tex]. This equation can be solved by isolating [tex]\( x \)[/tex].
2. Cross-multiply to eliminate the fractions: Cross-multiplying involves multiplying the numerator of each fraction by the denominator of the opposite fraction. This step transforms the equation into a form without fractions.
[tex]\[ -3 \times 24 = 4 \times x \][/tex]
3. Simplify the multiplication on the left-hand side: Perform the multiplication:
[tex]\[ -3 \times 24 = -72 \][/tex]
Now, the equation is:
[tex]\[ -72 = 4x \][/tex]
4. Solve for [tex]\( x \)[/tex]: To isolate [tex]\( x \)[/tex], divide both sides of the equation by 4:
[tex]\[ x = \frac{-72}{4} \][/tex]
5. Simplify the division: Perform the division to find the value of [tex]\( x \)[/tex]:
[tex]\[ x = -18 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(-18\)[/tex].
The correct answer is [tex]\(\boxed{-18}\)[/tex].
