Let's solve each equation step-by-step.
### First Equation:
[tex]\[
\frac{-10}{-14} = \frac{16x}{-14}
\][/tex]
1. Simplify both sides:
[tex]\[
\frac{-10}{-14} \quad \text{simplifies to} \quad \frac{10}{14} = \frac{5}{7}
\][/tex]
[tex]\[
\frac{16x}{-14} \quad \text{simplifies to} \quad \frac{-16x}{14} = -\frac{8x}{7}
\][/tex]
Thus, the equation now is:
[tex]\[
\frac{5}{7} = -\frac{8x}{7}
\][/tex]
2. To get rid of the denominators, multiply both sides by 7:
[tex]\[
5 = -8x
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = -\frac{5}{8}
\][/tex]
4. Simplifying gives us:
[tex]\[
x = -0.625
\][/tex]
So, the solution to the first equation is:
[tex]\[
x = -0.625
\][/tex]
### Second Equation:
[tex]\[
6x + 6(x + 6) = 96
\][/tex]
1. Distribute the 6 on the left side:
[tex]\[
6x + 6x + 36 = 96
\][/tex]
2. Combine like terms:
[tex]\[
12x + 36 = 96
\][/tex]
3. Subtract 36 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
12x = 60
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{60}{12}
\][/tex]
[tex]\[
x = 5
\][/tex]
Thus, the solution to the second equation is:
[tex]\[
x = 5
\][/tex]
### Summary:
The solutions to the given system of equations are:
[tex]\[
x = -0.625 \quad \text{(from the first equation)}
\][/tex]
[tex]\[
x = 5 \quad \text{(from the second equation)}
\][/tex]
