First, solve for \( \left|x + 4\right| \):

\( \left|x + 4\right| \) - 9 = -6
\( \left|x + 4\right| \) = -6 + 9
\( \left|x + 4\right| \) = 3

The value inside the absolute value brackets can be either positive or negative so (x + 4) must equal + 3 or -3 for \( \left|x + 4\right| \) to equal 3:

So, x = -7 or x = -1.

Betty scored 87% on the test meaning she earned 87% of the possible points on the test. There were 280 possible points on the test so she earned 280 x 0.87 = 244 points. Each question is worth 4 points so she got \( \frac{244}{4} \) = 61 questions right.

If the tiger has consumed 117 pounds of food in 9 days that's \( \frac{117}{9} \) = 13 pounds of food per day. The tiger needs to consume 182 - 117 = 65 more pounds of food to reach 182 pounds total. At 13 pounds of food per day that's \( \frac{65}{13} \) = 5 more days.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

The equation for this sequence is:

a_n = a_n-1 + 7

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 7
a₆ = 29 + 7
a₆ = 36