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 ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.

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

\( \left|x + 4\right| \) - 2 = -9
\( \left|x + 4\right| \) = -9 + 2
\( \left|x + 4\right| \) = -7

The value inside the absolute value brackets can be either positive or negative so (x + 4) must equal - 7 or --7 for \( \left|x + 4\right| \) to equal -7:

So, x = 3 or x = -11.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-7c^7}{4c^3} \)
\( \frac{-7}{4} \) c^{(7 - 3)}
-1\(\frac{3}{4}\)c⁴

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