Question 5

Question 5 Three students solved the equation 3(5x–14)=18 in different ways, but each student arrived at the correct answer. Select all of the solutions that show a correct method for solving the equation. I broke this question into different parts in order to go over each answer. Again, remind the student they need to get ALL answers right in order to get the points on the test. To solve this, the students may have to think outside the box to get the answer correct, since the problems are solved in different ways than they are used to seeing.

Question 5 Cont A) 3(5x – 14) = 18 8x – 14 = 18 This answer is incorrect. The student got the first step wrong. They added the 3 and 5, when they should be multiplying the 3 to both the 5x and – 14. The rest of the math on the page is correct, but the first step is wrong.

Question 5 Cont B) 1 • 3(5x – 14) = 18 • 1 3 3 5x – 14 = 6 + 14 + 14 This answer is correct. The students may be confused on this one because, for the most part, we do not see that in this type of problem. Most teachers have the students multiple the 3 to the numbers inside the parenthesis, but it is a valid way to solve it. Even the answer key states that it is not a common way to solve the problem so the students may think it’s wrong.

Question 5 Cont C) 3(5x – 14) = 18 15x – 42 = 18 15 15 15 +42 = + 42 15 15 x = 60 15 x = 4 This answer is also correct. The students will probably think it is solved incorrectly because it is solved in a different form than they are used to seeing. The distribution of the 3 to the 5x and – 14 is typical and the students should be used to seeing that. However, when most of us teach the students, we would not divide by the number in front of x until after adding 42 to both sides. This example shows that they divided first, and then added. The math is correct on this one and this is a correct answer. The answer guide states this is a correct way of solving but not a typical way.