Geometry

Given: 7x + 2 = 2 + 5x – 6
Prove: x = –3

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?
Answer
A. Commutative Property of Addition
B. Associative Property of Addition
C. Distributive Property
D. Addition Property of Equality

  1. 0
  2. 0
  3. 3
asked by Anonymous
  1. 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

    7x + 2 = 2 + 5x – 6
    7x + 2 - 2 - 5x = 2 + 5x – 6 - 2 - 5x
    7x - 5x = -6
    2x = -6
    x = -3

    after doing these for a few days, we were allowed to go
    7x + 2 = 2 + 5x – 6
    2x= -6
    x = -3

    1. 0
    2. 0
    posted by Reiny
  2. So which is the correct answer

    1. 0
    2. 0
    posted by Anonymous
  3. 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.

    1. 0
    2. 0
    posted by Jach
  4. Woops, I'm sorry, it's the Associative Property. Remember kids, double check your answers and watch out when answering even the most basic of math problems when you're sleep deprived!

    1. 0
    2. 0
    posted by Jach

Respond to this Question

First Name

Your Response

Similar Questions

  1. RESEARCH REPORT

    HI I WOULD LIKE TO KNOW WHAT I CAN POSSIBLY PROVE ABOUT EITHER THE BERMUDA TRIANGLE OR ATLANTIS THE LOST EMPIRE WE AARE SUPPOSED TO PROVE SUMTHIN ABOUT EITHER OF THOSE TWO CHOICES.... I ALSO NEED SITES THAT CAN HELP ME PROVE
  2. math

    My math teacher wants us to prove that all of our answers are correct. But how am I supposed to be able to prove stuff, like this, for example. The directions want you to write out the words in to an equation. Seven is the sum of
  3. math

    Prove that if A is a diagonalizable matrix, then the rank of A is the number of nonzero eigenvalues of A. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on
  4. math

    Let f:A->B, where A and B are nonempty, and let T1 and T2 be subsets of B. a.Prove that f^-1(T1 U T2)= f^-1(T1) U f^-1(T2). b.Prove that f^-1(T1 intersects T2) = f^-1(T1) intersects f^-1(T2). I think once I see a I can do b. c.
  5. Geometry

    Can you just help me with this thanks Directions: Tell which property is being used for each step I will give you an example Example: prove that if 4x-8=-8 then x=0 Given: 4x-8=-8 Prove: 0 A. 4x-8=-8 Given B. 4x-0 Addition
  6. history

    I'm supposed to prove that if america stopped getting involved in the affairs of the world the result would NOT be chaos. PLEASE HELP WITH ANY IDEAS ON HOW TO DO SO! It is not possible to prove a hypothetical. Can you prove that
  7. Science - Proof of Propositional Logics

    I am being asked if I can prove P, L, Q? (without using resolution-refutation). Propositional clauses: 1. P -> V 2. !P -> (!V and F) 3. (V or F) -> Q 4. Q -> L From here I was able, with resolution-refutation, to determine that we
  8. Math

    Find inverse of f if f(x)= x^2-4x+3, (for x is smaller than and equal to 2). First prove that f(x) is one to one in the defined domain of f and then obtain the inverse function. I know how to find the inverse. We just switch x and
  9. Math Proof

    Prove: Let a,b exist in the reals with a
  10. geometry

    prove that every every line segment has one and only one end point . use euclids geometry to prove
  11. Geometry

    Given: UR=VW Prove: UV=RW(Midpoint) Given: angleABE=angleDBC(Bisectors) Prove: angleABD=angleCBE

More Similar Questions