Final answer:
The solutions to the given equations are no solutions for x in Equation 8, m being 7.25 or -9 for Equation 9, and k being 5.6 or -2.4 for Equation 10.
Step-by-step explanation:
The solution to each equation is found by isolating the variable on one side of the equation.
Solution to Equation 7: n = ...
The question does not provide an explicit Equation 7; however, the reference to '2× 107 years' may relate to the solution but there's not enough context to solve for 'n'. Hence, we can't solve for 'n' without the full equation.
Solution to Equation 8: x = ...
For the equation |x| = -9, it's important to note that the absolute value of a number cannot be negative, hence there are no solutions for x in this equation.
Solution to Equation 9: m = ...
Starting from the equation |8m + 7| - 5 = 60, we first add 5 to both sides to get |8m + 7| = 65. Next, we recognize that the absolute value equation gives us two possibilities: 8m + 7 = 65 or 8m + 7 = -65. Solving both equations for m, we get m = 58/8 and m = -72/8, giving us m = 7.25 or m = -9.
Solution to Equation 10: k = ...
For the equation |5k - 8| / 10 = 2, we start by multiplying both sides by 10 to obtain |5k - 8| = 20. Again, we have two cases: 5k - 8 = 20 or 5k - 8 = -20. Solving for k in both situations gives us k = 28/5 and k = -12/5, which simplifies to k = 5.6 or k = -2.4.