Algebra: Plugging in Numbers

1. D

Plug a number less than -6 into each answer choice (don't do all the math, just look at the signs):

(A) $\dfrac{x^5}{-10}=\dfrac{-7^5}{-10}=\text{a negative } \div \text{ a negative = a positive!}$

(B) $-2x=-2\times-7=\text{positive}$

(C) $x+(^-x)=-7+(^-(-7))=0$

(D) $\dfrac{x^2}{x+5}=\dfrac{-7^2}{-7+5}=\text{square makes a positive } \div \text{ a negative = a negative}$

(E) $\dfrac{x}{-2}=\dfrac{-7}{-2}=\text {positive}$

2. E

$$\eqalign{a+b&=-20\\a&>-7\\\\-6+b&=-20\\+6&\;\;+6\\b&=-14}$$

Based on that, cross out: B, C, D

What if $a=10$?

$$\eqalign{a+b&=-20\\a&>-7\\\\10+b&=-20\\-106&\;\;-10\\b&=-30}$$

Now, cross out A.

3. D

(A) 3

$3(3-3)(3+7)=3\times0\times10=0$ 

(B)-7

$-7(-7-3)(-7+7)=-7 \times -10\times0=0$

(C)0  

$0(0-3)(0+7)=0\times-3\times7=0$

(D)-9

$-9(-9-3)(-8+7)=-9\times-12\times-1=\text{negative}$

(E)10

$10(10-3)(10+7)=10\times7\times17=\text{positive}$

4. 36 or $\dfrac{4}{9}$ or .444 or 2916

$4\centerdot 3 \centerdot 3 \centerdot \dfrac{3}{3}=36$

$4\centerdot 9 \centerdot 9 \centerdot \dfrac{9}{1}=2916$

$4\centerdot 1 \centerdot 1 \centerdot \dfrac{1}{9}=36$