The ROTC cadets traveled to Eglin Air Force base during a field trip the graph below show the cadets distance from Eglin

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heysorryguys

09.01.2023

Mathematics

Additive inverse: u=-x+24 , Multiplicative inverse: $v = \frac{1}{x-24}$

Step-by-step explanation:

According to real number algebra, the additive and multiplicative numbers are numbers such that:

w+u = 0 and $w\cdot v = 1$ , $\forall\,w,u,v\in \mathbb{R}$

If w = x-24 , then:

Additive inverse

1) x-24 +u=0 Given

2) $x+(-24)+u_{1}+u_{2} = 0$ Definitions of addition and subtraction

3) $x+u_{1} +[u_{2}+(-24)]=0$

4) $x+u_{1} = 0 \,\wedge\,u_{2}+(-24) = 0$

5) $u_{1} = -x \,\wedge\,u_{2} = 24$ Compatibility with addition/Additive inverse/Modulative property.

6) u=-x+24 By 2) and 5)/Result

Multiplicative inverse

1) $(x-24)\cdot v = 1$ Given

2) $v = (x-24)^{-1}$ Compatibility with multiplication/Modulative property/Multiplicative inverse

3) $v = \frac{1}{x-24}$ Definition of division/Result

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