Thursday, August 30, 2012

Study for the Assessment Tomorrow - One Last Review Problem

Here's one last review problem to see if you're ready for the assessment tomorrow over Solving Equations with Variables on Both Sides. Write it down and work it out, then click on the comments to this post to see the answer.

Solve:  5x - 7 = -8(2x - 3)

Please remember to prepare for the assessment tomorrow.

1 comment:

  1. OK, here's the worked out answer

    5x - 7 = -8(2x - 3)

    First thing we need to do is distribute that -8. That means we need to multiply the -8 by both the 2x and the -3. So we get:

    5x - 7 = -16x + 24 (be very careful with those signs)

    Now we want to get the variables to the same side by doing an inverse operation. We could either subtract 5x from both sides, or add 16x. I'm going to choose to add 16x.

    5x - 7 = -16x + 24
    +16x +16x

    21x - 7 = 24

    Now to isolate the 21x, I'm going to add 7 to both sides

    21x - 7 = 24
    +7 +7

    21x = 31

    Now I do the opposite or inverse of multiplying by 21, so I divide both sides by 21.

    21x = 31
    21 21

    So my answer is 31/21 (that's an improper fraction with 31 in the numerator and 21 in the denominator, hard to create it correctly in a comment).

    Don't forget you can always check your answer to an equation. To check it, you substitute your answer back in everywhere you see x, and then see if the two sides of the equation are equal.

    In this case, 31/21 is not the easiest thing to work with. So, you have two choices. Work with the fraction itself to be definitely sure, or get a decimal approximation and see if the two sides are really, really close (won't be exact since we're using an approximation, but should be close enough to make you feel confident you did it correctly).

    So, if you take 31 divided by 21, you get 1.4761905... Since we have calculators, I would suggest rounding that to 1.476 and using that to check. If I do that, then I would have:

    5(1.476) - 7 = -8(2[1.476] - 3)
    7.38 - 7 = -8(2.952 - 3)
    0.38 = -8 (-.048)
    0.38 = 0.384

    Note how they are not exactly equal, but that's what we would expect since we rounded our decimal approximation. But, since they are so close to each other, that gives me a fairly high level of confidence that my answer, 31/21, is correct. (Again, to be completely sure, I would need to keep it as 31/21 and work with the fractions.)

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