Mande's (hopefully helpful) Help Page
| ***All sections, except for the last, will follow the same format: an easy, medium, and hard problem, with the actual work shown on the right and comments on the left. Hope this helps! |
Solving Linear Equations Linear Equation: an equation that can be written in the form ax = b, where a and b are constants and a does not equal 0. |
| An Easy One | |
| Here is the first problem | 4x = 20 |
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| Get the variable by itself by dividing out the co-efficient, which in this case is the number 4. | 4x/4 = 20/4 |
| Now simply do the math. Your answer should be 5. Don't you feel smart? | x = 5 |
| Now let's try one a little bit Harder. | (x/3)- 4 = (x/5) |
| Because this is a problem with fractions, we first have to find the Least Common Denominator (pre-Algebra) | 3, 4, and 5 are all factors of 60 |
| Place the entire problem over 60 to give everything the same base | (x/3)*20 - 4*60 = (x/5)* 12 |
| Eww. That looks kinda nasty now, right? So why don't we simplify our lives a bit. | (20x/60)- (12x/60) = (240/60) |
| Now we can do the arithmatic.
Stick a fork in it...we're done!!! |
(8x/60) = (240/60)
8x = 240 x = 240/8 x = 30 |
| This next one is supposed to be a really Hard problem, but you've done so well so far that I doubt this will even phase you. | (9/5)*(3-x) = (3/4)*(x-3) |
| This problem can be done by finding the LCD. However, I think that the best way is to make everything into decimal form. | (1.8)*(3-x) = (.75)*(x-3) |
| Do you remember how to multiply multiple terms? | 5.4 - 1.8x = .75x -2.25 |
| Get like terms on the same side, then combine the like terms, again. | 5.4 - 1.8x + 1.8x + 2.25 = .75x -2.25 +
2.25 + 1.8x
5.4 + 2.25 = .75x + 1.8x 7.65 = 2.55x |
| Now finish up. | 7.65/2.55 = 2.55x/2.55
3 = x |
| (That wasn't really harder : it wasn't even long.) |
Solving Literal Equations Literal Equation: A problem composed mainly of variables which have standard meanings (F = force; t = time). A formula. |
| The formulas that will be used should be familiar to anyone old enough to be taking Algebra II. So I'll tell you what each variable represents so that the ideas will better stick to your mushy gray matter. | |
| The first will be easy, I hope. | d = rt, for t |
| This is the Distance Formula (not the math one, though). But of course you already new that. | d = distance r = rate t = time |
| So all I'm asking you to do is use the Distance Formula to isolate, or "find", the time. | d = rt, for t |
| Divide both sides by 'r' (rate). | d/r = rt/r |
| Now clean it up, and you're done. | d/r = t |
That was easy, right? |
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| Here's another familiar one | P = 2l + 2w, for w |
| This is the formula for finding the Perimeter of a rectangle. | P = perimeter l = length w = width |
| Use the Perimeter Formula to find 'w' (width) | P = 2l + 2w, for w |
| Subract 2 times the length from each side. | P- 2l = 2w |
| Now divide both sides by 2 to leave 'w' by itself. | (P- 2l) / 2 = w |
| You're finished!! | |
| Now this last one maybe not be recognizable at first, but I'll explain. | a = (vf - vi) / t , for vf |
| This is the Acceleration Formula. Ring a bell? | a = acceleration; vf = final velocity; vi = initial velocity; t = time |
| Use the Acceleration formula to find vf | a = (vf - vi) / t , for vf |
| Multiply both sides by 't' | a*t = vf - vi |
| Add 'vi' to both sides to leave vf alone.
And you now know how to solve Literal Equations (let's hope). |
at + vi = vf |
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Writing the Equation for a Line... (8, 5) (11,14) We're going to find the equation of a line using the following three linear equation forms: The most common form
is Slope-Intercept Form (y = mx+b).
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| You have been given two points. Our first job is to find the slope. | (y2
- y1) / (x2 - x |
| This means "(y of the first point - y of the second point), divided by (x of the first point - x of the second point) = the slope | |
| Plug in your x's and y's | (14 - 5) / (11 - 8) =m |
| Now clean it up. | 9/3
3 = m |
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Slope-Intercept Form |
y = mx + b |
| You already have the slope, so the problem should read... | y = 3x + b |
| Now to find the y-intercept ( b), substitute one of the original points....(8,5) | 5 =3(8) + b
5 = 24 + b |
| Clean it up and you're done. | b = -19
y = 3x - 19 |
| Point Slope Form | y - y1 = m(x - x1) |
| First, plug in what you already have. | y - y1= 3(x - x1) |
| Now substitute the first point.
And distribute. And finish up. |
y - 5 = 3(x - 8)
y - 5 = 3x - 24 y = 3x - 19 |
| Standard Form | ax + by = c |
| Using one the the other form's final answers, get your x's and y's on the same side. | -3x + y = -19 |
| You can't have a negative 'x', so divide both sides by -1, and you're finished. | 3x - y = 19 |
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