Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10 given ⇒ 2(x − 4) + 6x = 9x − 10 step 1 ⇒ 2x − 8 + 6x = 9x − 10 step 2 ⇒ 2x + 6x − 8 = 9x − 10 step 3 ⇒ 8x − 8 = 9x − 10 step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10 step 5 ⇒ 0 − 8 = x − 10 step 6 ⇒ −8 = x − 10 step 7 ⇒ −8 + 10 = x − 10 + 10 step 8 ⇒ 2 = x + 0 step 9 ⇒ 2 = x which step in solving this equation is justified by the distributive property? a) step 1 ⇒ 2x − 8 + 6x = 9x − 10 b) step 2 ⇒ 2x + 6x − 8 = 9x − 10 c) step 3 ⇒ 8x − 8 = 9x − 10 d) step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10

Step 1

Step-by-step explanation:

You distributed the 2 in 2(x-4) to get 2x-8

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).