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19 votes
19 votes
Kelsey solved the following equation:

7x − one over two (8x + 2) = 6

Step Work Justification
1 7x − 4x − 1 = 6
2 3x − 1 = 6
3 3x = 7
4 x = 7 over 3
Which of the following has all of the correct justifications Kelsey used to solve this equation?

Question 8 options:

1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality


1. Multiplication property of equality 2. Combine like terms 3. Addition property of equality 4. Division property of equality


1. Distributive property 2. Combine like terms 3. Subtraction property of equality 4. Division property of equality


1. Multiplication property of equality 2. Combine like terms 3. Subtraction property of equality 4. Division property of equality

User Leodido
by
2.7k points

2 Answers

22 votes
22 votes

Answer:1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality

Explanation:

User Xiangkun
by
3.2k points
22 votes
22 votes

9514 1404 393

Answer:

(a) 1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality

Explanation:

Replacement of -1/2(8x +2) by -4x -1 is use of the distributive property, eliminating choices B and D.

In step 3, addition of 1 to both sides of the equation is use of the addition property of equality, eliminating choice C. This leaves only choice A.

_____

Additional comment

This problem makes a distinction between the addition property of equality and the subtraction property of equality. They are essentially the same property, since addition of +1 is the same as subtraction of -1. The result shown in Step 3 could be from addition of +1 to both sides of the equation, or it could be from subtraction of -1 from both sides of the equation.

In general, you want to add the opposite of the number you don't want. Here, that number is -1, so we add +1. Of course, adding an opposite is the same as subtracting.

In short, you can argue both choices A and C have correct justifications. The only reason to prefer choice A is that we usually think of adding positive numbers as addition, and adding negative numbers as subtraction.

User Ian Lundberg
by
2.4k points
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