How do you solve 18x + 9 = 9x + 42?

Question

Which of the following best describes the solution to the equation below?

18x + 9 = 9x + 42

 A.

exactly one real solution, 
 

 B.

no real solutions
 

 C.

exactly one real solution,

 D.

infinite real solutions
 

Comments

Two freight trains are delivering cargo. One freight train is delivering coal, and the other freight train is delivering grain. Their respective distances traveled after x hours is represented in the table and graph below.

Coal Freight Train Time (Hours) Distance Traveled (Miles) 1 47 2 94 3 141 4 188

Which freight train is traveling at a faster speed? A.

The coal freight train is traveling at a faster speed.
 

 B.

Both freight trains are traveling at the same speed.
 

 C.

There is not enough information to determine the speed of the trains.
 

 D.

The grain freight train is traveling at a faster speed.
 

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I have more:

Which of the following best describes the solution to the equation below?

 A.

exactly one real solution, 
 

 B.

no real solutions

 C.

exactly one real solution, 
 

 D.

infinite real solutions
 

Which of the following best describes the solution to the equation below?

 A.

infinite real solutions

 B.

exactly one real solution,

 C.

exactly one real solution,

 D.

no real solutions

Answer 1

Answer C: 18x-9x=42-9, 9x=33, x=33/9, x=11/3=3⅔.

Speed of grain train from graph is 45mph. Speed of coal train from table is 47mph (A).

No real solutions (B, because the variable terms cancel out).

Answer B, 5⅗.