Simplifying Exponential Expressions.
Find the value of X:
2^2+4x-7x^2=4x-2+7x
First, we must find any likes and cancel them out like that 4x. You could also combine the likes together. the equation would end up like 2^2-7x=-2+7x or 2^2-3x=11x-2. Add 7x to the first equation to get 4=-2+14x. x in this case would = to 2.3 repeated. Add 3x to the second equation to get 4=14x-2 where x would also = to 2.3 repeated. If you get stuck on 3*2=2x/4, multiply both sides by 4 to eliminate the /4. 3*2*4=2x=24/2=12. x would =12.
2^2+4x-7x^2=4x-2+7x
First, we must find any likes and cancel them out like that 4x. You could also combine the likes together. the equation would end up like 2^2-7x=-2+7x or 2^2-3x=11x-2. Add 7x to the first equation to get 4=-2+14x. x in this case would = to 2.3 repeated. Add 3x to the second equation to get 4=14x-2 where x would also = to 2.3 repeated. If you get stuck on 3*2=2x/4, multiply both sides by 4 to eliminate the /4. 3*2*4=2x=24/2=12. x would =12.
Closed Sets.
Closed sets mean that when you multiply something by that same thing, it'll always end up as something. For example. an integer subtracted/added/multiplied to another integer gets you another integer. But it you divided an integer by another integer, you might end up with some decimal number. Take 3 and 2 for examples. 1, 5, 6, and, uh oh, 1.5. All except 1.5 are whole numbers.
Multiplying Polynomial Expressions.
(4x + 3)(6x - 7), simplify. You just take a number and multiply it with the other 2 numbers. 4x * 6x = 24x^2, 4x * -7 = -28x, 3 * 6x = 18x, and 3 * -7 = -21. Then you add the likes; -28x+18x=-10x. the final equation would be 24x^2-10x-21.
Absolute Value Equations.
OK, so you know the basics like |-7|=7. How about finding the value of x through |2x-3|=12. Think of it as 2x-3=-12 as well since it doesn't matter if the number in the absolute value is positive or negative. 12+3=15, 15/2=7.5. -12+3=-9, -9/2=-4.5. X could equal 7.5 or -4.5. Just solve.