How do you solve #8k - 3( k - 5) = 45#?

Question

Kennedy Adams · Accepted Answer

See a solution process below:

First, expand the terms in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis: #8k - color(red)(3)(k - 5) = 45# #8k - (color(red)(3) xx k) - (color(red)(3) xx -5) = 45# #8k - 3k - (-15) = 45# #8k - 3k + 15 = 45# #(8 - 3)k + 15 = 45# #5k + 15 = 45# Next, subtract #color(red)(15)# from each side of the equation to isolate the #k# term while keeping the equation balanced: #5k + 15 - color(red)(15) = 45 - color(red)(15)# #5k + 0 = 30# #5k = 30# Now, divide each side of the equation by #color(red)(5)# to solve for #k# while keeping the equation balanced: #(5k)/color(red)(5) = 30/color(red)(5)# #(color(red)(cancel(color(black)(5)))k)/cancel(color(red)(5)) = 6# #k = 6#

Kennedy Adams · Answer

undefined To solve the equation 8k - 3(k - 5) = 45, first distribute the -3 across the parentheses to get 8k - 3k + 15 = 45. Then, combine like terms to get 5k + 15 = 45. Next, isolate the variable by subtracting 15 from both sides to get 5k = 30. Finally, divide both sides by 5 to solve for k, which gives k = 6.