To solve for \( x \) in the equation
[tex]\[
\frac{7x}{-10} = \frac{-42}{5},
\][/tex]
we follow these steps:
1. Clear the fraction by eliminating the denominator on the left-hand side. To do this, multiply both sides of the equation by \(-10\):
[tex]\[
\left(\frac{7x}{-10}\right) \cdot (-10) = \left(\frac{-42}{5}\right) \cdot (-10)
\][/tex]
This simplifies to:
[tex]\[
7x = \left( \frac{-42}{5} \right) \cdot (-10).
\][/tex]
2. Calculate the right side:
[tex]\[
\left( \frac{-42}{5} \right) \cdot (-10) = \frac{-42 \cdot -10}{5} = \frac{420}{5} = 84.
\][/tex]
So now we have:
[tex]\[
7x = 84.
\][/tex]
3. Solve for \( x \) by isolating \( x \) on one side of the equation. Since \( 7x = 84 \), divide both sides by 7:
[tex]\[
x = \frac{84}{7}= 12.
\][/tex]
Thus, the solution to the equation is:
[tex]\[
x = 12.
\][/tex]
Therefore, [tex]\( x = 12 \)[/tex]. The provided answer [tex]\( x = 6 \)[/tex] is incorrect. The correct answer is [tex]\( x = 12 \)[/tex].
