Algebra. You may like it, you may hate it. You may have left it behind years ago, or you may still use it every day. But one thing's for certain.
Algebra is only the second subject in math that you learn after arithmetic. Therefore, it's pretty safe to say that humans agree that it's the second easiest subject in math. Let's learn it in five minutes. This is a variable. What makes it a variable is that it's not represented with characters that could imply a constant number.
A variable is just a numeric value that we don't know yet. That's it. A variable can be written with any letter or character.
that isn't numeric, but most often we use x. Why x? Why not x? Variables also have a context.
It is assumed that for every new problem, the context for variables are reset. Therefore, x will be one specific value for one question, and maybe another value for another question. But within that question, x remains the same value.
It's also worth mentioning that using the variable x makes the use of an x as a multiplication sign very confusing. So, we'll represent multiplying two constants together with a dot or asterisk, and will represent a constant being multiplied by a variable with, well, nothing actually. A number next to a variable shows multiplication.
Back when you learned order of operations, if you saw a problem that looked like this, you evaluated it in these steps. So, that means that the following problems are functionally the same. This introduces the concept of the equal sign, which implies that the terms on the left side of the equal sign are equivalent in value to the terms on the right side. right side of the equal sign. The equal sign also introduces the next concept, equalities.
For example, variables may not necessarily start isolated. You may have an equality that looks like this, 2x plus 4 equals 16. Since we wanted to know what x is, we need to reverse engineer this equality. And by that, I mean we literally need to solve the problem by using order of operations in reverse. Now the big question, how do we do that?
Well, let's look at an obvious equality. For 4 equals 4. This is a true statement. If we add, subtract, multiply, or divide any number from both sides of this equation, we still get a true statement. 4 is still equal to 4, 5 is still equal to 5, 3 is still equal to 3, 6 is still equal to 6, and 2 is still equal to 2. So going back to the problem that we had before, we solve it by using order of operations in reverse, and adding, subtracting, multiplying, or dividing values to both sides of the equation.
sides of the equation to make effectively nothing different. If we subtract 4 from both sides of this equation, we get 2x equals 12. Then if we divide both sides of the equation by 2, we get x equals 6. Then if we look really carefully, we can see what x is. Don't worry, order of operations is really easy to remember if you just remember this expression.
Punch every mattress, destroy all sin. Or in this case, when it's in reverse, sin all destroy mattress every punch or my personal favorite nice law or search time here right no so now when you see those posts from 2010 that say 95% of people get this question wrong you can prove that you're in the top 5% by showing a basic competency in eighth grade algebra in addition to equalities there's also inequalities like this one and the way to solve inequalities is very similar to solving equalities there are only two main differences the first main difference is is that the result of solving the inequality tells you instead that a variable is any number larger or smaller than some specific value, rather than being exactly equal to that specific value. And the other difference is, because the meaning of the result has changed, any time you multiply or divide both sides of the equation by a negative number, the sign flips. So first we subtract 5 from both sides, then we divide both sides by negative 3. One of the best parts about algebra is that after finding a variable's value, you can check your answer by substituting in any legitimate value for x.
But let's not do that because it's basically just solving the same problem again. Let's look at a system of equations. You can think of a system of equations as a puzzle that can be solved. You can solve this puzzle guaranteed as long as at least as many unique equations exist as variables in the system of equations. For example, in this problem, you can look at the second equation and add y to both sides, leading to x equals y plus 3. We can then look at...
at the other equation replacing every instance of x with y plus 3. So here you see a showcasing of distribution in which 2 got multiplied by both y and 3. Now that we know y equals 2, we can substitute 2 for y in the second equation, giving us x minus 2 equals 3, or x equals 5. So x equals 5, and y equals 2. And that's a wrap on algebra! Have fun with your newfound knowledge, or oldfound knowledge.