Answer: a = -5
Step-by-step explanation:
First, open up the brackets, and solve it
-12a -42 = -22 -8a. (-6 x 2a, and -6 x 7)
bring the -8a to the left side, so that all the a’s are together
-12a -42 + 8a = -22 (add -42 on both sides like we did with -8a)
-12a + 8a = -22 + 42
solve
-4a = 20
divide -4 on both sides
a = -5
We're given

which immediately tells us that

In other words, swapping the limits of the integral negates its value.
Also,

The integral we want to compute is

which we can do by splitting up the integral at x = 4 and using the known values above. Then the integral we want is

Answer:
<h2>8(7n - 2) - 6(7n + 1) = 14n - 22</h2>
Step-by-step explanation:
8(7n - 2) - 6(7n + 1)
use the distributive property: a(b + c) = ab + ac
= 8 · 7n + 8 · (-2) + (-6) · 7n + (-6) · 1
= 56n - 16 - 42n - 6
combine like terms
= (56n - 42n) + (-16 - 6)
= 14n - 22