QuizBee-Q2Week3

Linear Equations in One Variable

Week 3

Quiz Bee

1. Answer the following questions. (10 questions in total)

2. Answer them within the given time. The faster you answer, the better points you have.

3. If you got the highest score, you will receive a reward. If you got a perfect score, you get a bonus point for our exam.

Multiple Choice

What property states that a number is equal to itself?

• Identity Property

• Reflexive Property

• Symmetric Property

• Transitive Property

Reflexive Property

This property states that for any real number a,        

 $a=a$   

Multiple Choice

What property is used to make x+1 = 4x+1 to become x = 4x?

• Cancellation

• APE

• MPE

• Transposition

Cancellation property of addition

 $x+1=4x+1$  
         ↑                ↑      (will be cancelled since they are the same term)
So, what will be left is:
 $x\ =\ 4x$  

Solution:

 $7-x=10$  (Given)
 $7-10=x$  (Transposition)
 $-3=x$  (Simplified LHS)
 $x=-3$  (by Symmetric Property)

Multiple Choice

What kind of linear equation has infinitely many solutions?

• Conditional

• Contradiction

• Identity

Identity

For this kind of linear equation, we should know that any value of the variable will make the equation true. Thus, its solution set is the set of all real numbers.

Multiple Choice

What kind of linear equation is the given below?

 $3x\ =\ -3x$  

• Conditional

• Contradiction

• Identity

Solution:

 $3x=-3x$  (Given)

 $3x+3x=0$  (Transposition)

 $6x=0$  (Simplifying the LHS)

 $\frac{6x}{6}=\frac{0}{6}$  (MPE)

 $x=0$  

Since x can only be 0, therefore, the given equation is CONDITIONAL.

Conditional

It is a conditional linear equation (in one variable) when one and only one value can satisfy the given equation.

Solution:

 $3a−1=a+5$  (Given)

 $3a-a=5+1$  (Transposition)

 $2a=6$   (Simplify)

 $\frac{1}{2}\left(2a\right)=\left(6\right)\frac{1}{2}$  (MPE)

 $a=3$    

Solution:

  $3(p−2)−(4−p)=10$  (Given)
 $3p-6−4+p=10$ (DPMA)
 $4p-10=10$  (Simplify)

 $4p=10+10$  (Transpose)
 $4p=20$  (Simplify)

 $\frac{4p}{4}=\frac{20}{4}$  (MPE)

 $p=5$   

Solution:

 $3\left(2f-4\right)+2\left(5-3f\right)=2$  (Given)
 $6f-12+10-6f=2$  (DPMA)
 $-2=2$  (Simplify)
 $-2\ne2$  (Contradiction)

Thus, the solution set for the given equation is { }.

Contradiction

A contradiction linear equation is an equation that doesn't have any element in the solution set as all values will not satisfy the sentence.

Multiple Choice

What is the value of k in the equation below when the solution to the given statement is y=16?

 $ky-6=8$  

•  $\frac{5}{6}$  

•  $\frac{7}{8}$  

•  $\frac{8}{7}$  

•  $\frac{6}{5}$  

Solution:

 $ky-6=8$  ,  $y=16$  
 $k\left(16\right)-6=8$  (Replace the value of y)
 $16k=8+6$  (Transpose)
 $16k=14$  (Simplify)
 $\frac{16k}{16}=\frac{14}{16}$  (MPE)
 $k=\frac{7}{8}$  

TRIVIA

UNESCO proclaimed on November 2019 that 14th of March of every year will be the International Day of Mathematics. March 14 is also considered in many places as "Pi Day" representing the first couple of digits of the number-- 3.14.