Rules to Remember Flashcards
If you are solving for x in an equation that typically have a denominators look like this (x-4 or x+3x+9) and the question is telling you “if there is more than one solution, sepearate them with commas. If there is no solution click No solution” What steps should you take?
Find the LCD and then EXCLUDE the values, so if we get them in the answe, we don dont type them
When solving for an equation such as (10x-1)^3/4 what two rules should you rember (hint: x^2=c)
Rule 1: Both will be raised to an even number which means you must check the answer in case there are other solutions.
Rule 2 : If the number is negative click on “No solution” and if it positive there will be two solutions + and -
If you get in you answer 0=3 or any number, what does that mean?
No solution
If you get in you answer 0=0 or any number, what does that mean?
All real numbers are solutions
When you get an equation looks like this (-35=-7/5 w) and it is asking you to solve for w what should you do?
Multiply the reciprocal of -7/5 which is -5/7, on both sides
-3-5i conjugate is
-3+5
You will need to multiply it with the denominator.
Use it when solving proplems such as 1-3i/-3-5i. to multiply both with the conjugate -3+5
When you get an equation such as y+2/7 = 5/4 what method can you use to solve it?
Method of cross product 4(y+2) = 5.7
When you are asked to find the Discriminant and the Number of real number with an equation looks like this 9x^2-6x+1, what should you do?
Use the equation under the square root of the quadratic formula which is b^2 - 4(a)(c) and start solving. If the answe was a positive number, the number of real numbers is 2, if the answer is negative the number of real numbers is 0, if the answer is 0 then the number of real numbers is 1
How to solve i^59
The factor 2 cannot give us a 59 product, so in this case we will do the following i^58 i then (i)^29 because 2x28=58. Then we will use the fact i = -1 and do the following (-1)^29 i ,we cancel the 29 and get the following (-1) i which give us the following answer -i
What should you do when you face a shape that gave you the perimeter and asking you to find the value of x
add all the equations that is shown on the shape sides and solve the equation
How to solve D= 4/7(F+G) Which have only one denominator
Since it have the numenator and denominator as real numbers4/7 Ww will multiply it in both sides (when multiplying we convert the numenator with the denominator) and solve we will get 7/4 D-G = F
ALWAYS REMEMBER WHEN SOLVING A RATIIONAL EQUATION TOOO:
Find the LCD and exclude the valuse, so if I got the exluded value when answerimng the equation, then I should select “No answer” or not write it down.
If a equation asks you to find how much a (something) will be produce in a set of time (such as 45min) if it is usually produces 240 in 25 min. What should you do?
Divide the quantity (240) with the time (25) 240/25 = 9.6. Then I will multiply the answer (9.6) with th time (45 min) which gives me 432
How to multiply (-6+5i)(-3+3i)?
We use the FOIL method (18-33i+15i^2) and then we convert the last number which has i^2 (since i^2 is -1, 15i^2 is -15, and so on) and then we subtract the first and last numbers (the 18 and -15 which give us a 3) The final answer will be 3-33i which is a complex number
-3 square root will be
i with 3 as a square root (the i should be behind the square root not after)
What should be the first step to solve this quation (w-3)^2=2w^2-15w+27
(EQUATION)^2= EQUATION
The first step should be to move the (EQUATION)^2 to the other side WITH SIGNS if it was positive than it should be negative. It should look like this 0= EQUATION(EQUATION)^2 and then you use the FOIL method to solve the (EQUATION)^2 and then you continue to solve the equation.
What steps should you take to find the area of a rectangle? (e.q area 52 and length is 5 less than double the width)
REVIEW THIS
Solving a word problem using a quadratic equation with rational roots
First write the equation for the length which in this case will be L=2w-5, convert the L to W with will be (2w-5)w= 52 and start to solve for the width. To solve for the length you need to solve using L=2w-5. Take the answer you got from the width which will be 6.5 and solve it.
How to solve the following -4 |w| = 12
We have to move the -4 to the other side (the 12) and we will doing this be dividing 12/-4 which will give us |w| = -3 since it is negative the answer will be “No solution but if it was positive the answer will be w= 3,-3
How to solve the following -3+square root of w+3 = 6
First we move the -3 to the other side and it will give us 9. To cancel the square root we have to square both sides to a power of 2, and we will get the following w+3=9^2 then w+3=81. To solve w we have to move the 3 to the other side and the final answer will be w = 78
FOUCUS ON SIGNS
ok
Always let the number with i in the last such as
8i + 4 should be 4 + 8i
How to solve the following problem 5u^2+15u=0
Sinc ther is a u in both sides we will simplify it to 5u(u+3). Then the equation will only be true if one of them is equal to 0. So, 5u= 0 and u= -3. Our answer will be u= 0, -3** (WRITE THE 0)**
How to solve the following equation |5u - 6| = |9u + 2|
We have to solve this equation using** two diffrent types of soultions. The first we will take of the vertical | and start to solve, in this euation we will get -2 (some time it could be false and does not have any solution)** The second one we will take off the vertical |, but this time** the equation on the right side will be multiplyed with negative one -** {e.q - (9u + 2)} and you include both answers in the final answer.
How to solve the following equation -6 |x| = -36
If the -6 was in the other side e.q |x| -6 we will use the opposite signel and move it to the other side of the equation. But, because it is -6 |x| we will divide it with the -36 so it will be -6|x|/-6 (which will cancel it and let the |x| alone) and -36/-6 and that will give us 6. So the final answer will be |x| = 6, -6
Rule to remeber with eqations that have a variable on it denominator or numinator and a number on it* denominator or numinator *
In this case we multiply each number in the equation with the denomiantor whether it is a number or variable. If all were varibales or numbers e.q 2/3 then in this case we will multiply the sides of the equation with 3/2. Which is the opposite of 2/3
