The dot plots below show the scores for a group of students who took two rounds of a quiz: Two dot plots are shown one below the other. The title for the dot plot on the top is Round 1 and the title for the bottom plot is Round 2. Below the line for each dot plot is written Score. There are markings from 5 to 9 on the line at intervals of one. There are 2 dots above the mark 5, 3 dots above the mark 6, 4 dots above the mark 7, and 1 dot above the mark 8. For the bottom dot plot there are 6 dots above the mark 6, 2 dots above the mark 8, and 2 dots above the mark 9. Which of the following inferences can be made using the dot plot? The range of each round is the same. There is no overlap between the data. Round 1 scores were higher than round 2 scores. Round 2 scores were lower than round 1 scores.

answer is x<

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.