How to solve for the variable "X"
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
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.
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