|3x+7|= -15

2. |b+5|=2b-9

1. The absolute value function takes any quantity and makes it positive, so it's impossible to have |3x + 7| < 0. There is no solution.

2. If b + 5 ≥ 0, then

|b + 5| = b + 5 = 2b - 9

b = 14

Otherwise, if b + 5 < 0, then

|b + 5| = -(b + 5) = 2b - 9

-b - 5 = 2b - 9

3b = -4

b = -4/3

However, this second solution is extraneous, since the left side is positive,

|-4/3 + 5| > 0

while the right side is negative,

2•(-4/3) - 9 = -8/3 - 9 < 0

15.5

step-by-step explanation:

5

∑

n = 1

substitute n = 1, 2, 3, 4, 5 and sum the terms

= + + + 2² + 2³

= 0.5 + 1 + 2 + 4 + 8

= 15.5

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1