Algebra

Question 1

Expression

Answer 1

Does not have an = sign

Question 2

Denominator trick

Answer 2

If your equation contains a denominator,

• Put parentheses around the ENTIRE equation, and
• MULTIPLY it by the denominator

If the equation contains MULTIPLE DENOMINATORS
- Eliminate them by multiplying by the lowest common denominator (LCD)

Question 3

When to cross-multiply?

Answer 3

If one fraction equals another

(x+1)/3 = (2x-5)/4

Question 4

When working with inequalities, beware of…

Answer 4

Multiplying or dividing by a variable (you may need to flip the sign!)

Must consider BOTH scenarios (negative variable, positive variable)

Question 5

Compound inequalities - how to isolate the variable in the middle?

Answer 5

Do the same thing to all 3 sides

Question 6

How to solve an equation with variables AND numbers inside the absolute value brackets?

Answer 6

1. Isolate the absolute value brackets
2. Drop the brackets, and place +/- sign in front of the algebra (NOT in front of the answer)
3. You will then get 2 equations (2 possible answers) - solve for both of them
   BUT BEWARE THAT BOTH ARE NOT ALWAYS VALID

Question 7

Elimination strategy when solving 2 equations (with >1 variable)

Answer 7

1. Stack the equations atop one another
2. Arrange the variables in the same order
3. Add or subtract equations to ELIMINATE one of the variables

If necessary, MULTIPLY one (or both) of the equations by some value to give either variable opposite coefficients

Question 8

Equations with even exponents…

Answer 8

…Have 2 solutions

(x-3)^2 = 25
Then,
x-3=5 and x-3=-5

Question 9

Taking the root of an even exponent

Answer 9

Results in an absolute value

Question 10

Quadratic functions - how to solve?

x^2 + 3x + 1

Answer 10

1. Set equal to 0
2. Make sure the x^2 term is positive
3. Factor

(x ) (x )

Numbers should MULTIPLY to the LAST value, and ADD to the MIDDLE value

Question 11

Quadratic functions - what is a solution?

Answer 11

Same as the “root” - the answer to both of the factors

Question 12

Factors of a quadratic equation?

Answer 12

Set each factor to 0 and solve.

X^2 + 7X + 10 =0 –> (X+2)(X+5) these are the “factors”

X+2=0 and X+5=0

X=-2 and X=-5 these are the “roots” aka “solutions”

Question 13

(x + 2)(x + 3) = 0

How to solve for x?

Answer 13

DO NOT FOIL! This quadratic has already been factored. Set each factor = 0 and solve for the “roots” or “solutions.”

Question 14

(x + y)^2

Answer 14

x^2 + 2xy + y^2

X squared + 2xy + y squared

Question 15

(x - y)^2

Answer 15

x^2 - 2xy + y^2

Question 16

(x + y) (x - y)

Answer 16

x^2 - y^2

Question 17

Plug in question

Answer 17

The comparison of expressions (variables can have limitless or nearly limitless values)

Goal is to prove an inconsistent relationship between the 2 quantities

Always test at least 3 values (generally -1, 0 and 1 if possible)

Remove any items shared by the two expressions

Question 18

Manipulating algebra for a “plug-in” question

Answer 18

1. Add or subtract anything you want from both sides
2. Multiply or divide both sides by a POSITIVE value
3. Square or square root both quantities - IF they are positive

Question 19

To solve an equation with TWO denominators

Answer 19

Multiply the ENTIRE equation by the LCD