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    How to solve for the variable "X"

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    How to solve for the variable "X"

    The following problems have tripped me up. I can't seem to figure out how to solve them. I've tried, several times, and had my algebra teacher explain them, but I still can't get the answers.

    3x - 11 = 6
    2x - 7 = 3 + x
    3 + 3x = 9 + 2x
    3x - 3 = 6 + x

    © BrainMass Inc. brainmass.com December 24, 2021, 5:15 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/how-solve-variable-37886

    SOLUTION This solution is FREE courtesy of BrainMass!

    Basic Tips for Solving Equations

    Suppose I start with something like

    x = 5

    That's no fun, is it? There's nothing to figure out. But I can multiply both sides of the equation by 3 without changing the truth of the equation, right?

    3x = 15

    And there are a lot of different ways I can write 3:

    3 = 1 + 2

    = 7 - 4

    = -5 + 8

    So I can change my equation to look like this:

    3x = 15

    x(3) = 15

    x(7 - 4) = 15

    7x - 4x = 15

    And since I can add or subtract anything on both sides of an equation without changing the truth of the equation, I can add 4x to both sides:

    7x - 4x = 15

    7x - 4x + 4x = 15 + 4x

    7x = 15 + 4x

    And of course, I can do the same thing with any number I want:

    7x = 15 + 4x

    7x - 5 = 15 + 4x - 5

    7x - 5 = 15 - 5 + 4x

    7x - 5 = 10 + 4x

    Now I have something that looks just like your problems, don't I?

    The trick, then, is to reverse the steps that I just did, to get back
    to the original, simple, boring equation:

    7x - 5 = 10 + 4x

    7x - 5 + 5 = 10 + 4x + 5 Add 5 to both sides

    7x = 15 + 4x

    7x - 4x = 15 + 4x - 4x Subtract 4x from both sides

    3x = 15

    (3x)/3 = 15/3 Divide both sides by 3

    x = 5

    It's easy to forget what's really going on when you're solving an algebraic expression for a variable. You're really just trying to rewrite a complicated expression in a simpler way, without doing anything to change the meaning of the expression. It's a little like what you would do to change a complicated sentence like:

    "Under a mammal of feline persuasion is located, at this time, in an unspecified location, a rectangle of woven fabric."

    into a simpler one like:

    "The cat is on the mat."

    Algebra is basically tying knots and then untying them again.

    With that in mind, let's look at one of your example problems:

    3 + 3x = 9 + 2x

    The first thing to notice is that we have numbers on both sides. We know that someone put them there by adding a number to both sides of the equation, so we can un-put them there by subtracting a number from both sides:

    3 + 3x = 9 + 2x

    3 + 3x - 3 = 9 + 2x - 3

    (3 - 3) + 3x = (9 - 3) + 2x

    3x = 6 + 2x

    Now we have multiples of x on both sides. We can do the same kind of thing to fix that:

    3x = 6 + 2x

    3x - 2x = 6 + 2x - 2x

    (3 - 2)x = 6 + (2 - 2)x

    x = 6

    Can you follow the same kinds of steps to solve the rest of the problems?

    I hope this helps.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:15 pm ad1c9bdddf>
    https://brainmass.com/math/basic-algebra/how-solve-variable-37886

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