Given the equation 7x + 2 = 2 + 5x – 6, use the commutative property to rearrange the terms so that like terms are next to one another. This gives the equation 7x + 2 = 2 – 6 + 5x. Then, use the ____________________ to group the like terms. This gives the equation 7x + 2 = (2 – 6) + 5x. Next, combine like terms to get the equation 7x + 2 = –4 + 5x. Use the subtraction property of equality to subtract 5x from both sides of the equation. This gives the equation 2x + 2 = –4. Then use the subtraction property of equality again to subtract 2 from both sides of the equation. This gives the equation 2x = –6. Finally, use the division property of equality to divide both sides of the equation by 2 to give a final solution of x = –3. Therefore, given the equation 7x + 2 = 2 + 5x – 6, x is equal to –3.
Which justification was left out of the paragraph proof above?
A. Commutative Property of Addition
B. Associative Property of Addition
C. Distributive Property
D. Addition Property of Equality
If I had been faced with the above approach to solving simple equations of this type, I probably would have learned to hate math.
Fortunately I had good teachers who simply said,
"Whatever you do to one side of an equation , you must do to the other side" , so
I agree with Reiny, but he missed the point that this is an exercise in tedious proof that you'll never thankfully have to do again.
Commutative Property of Addition is the answer.
Because it's what lets you group things.
Since a lot of this is just pattern-matching rather than logic or computation, here's a tip. If you google each property, only Commutative and Distributive have anything to do with parentheses. Distributive has to do with multiplication and addition, while the Commutative is one or the other alone, so it's that one.
If you want a funner example of a proof, check out the proof by differential equation of e^(i*pi) = -1. There are of course thousands of other proof styles and millions of other proofs of different things. Just don't believe this style of proof is what mathematicians do.
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