Home >> Tests & Exam >> GRE : # Things you should know in algebra before GRE

**Example**

__-3x + 5 < 23__

for above inequality we need solutions for x.. above equation is equivalent to -3x < 18 or -x < 6 which means x > -6

hence x can be -5,-3.. 1,2... (infinite values)

- (x+y)
^{2}= x^{2}+ y^{2}+ 2xy - (x-y)
^{2}= x^{2}+ y^{2}- 2xy - (x+y)
^{3}= x^{3}+ y^{3}+ 3xy(x + y) - (x-y)
^{3}= x^{3}- y^{3}- 3xy(x - y) - x
^{2}- y^{2}= (x + y)(x - y) - x
^{-2}= 1/x^{2}, 2^{-4}= 1/16 = 1/2^{4} - (x
^{a})(x^{b}) = x^{a+b} - x
^{a}/x^{b}= x^{a-b}= 1/x^{b-a} - x
^{0}=1 - x
^{a}y^{a}= (xy)^{a}, 2^{2}3^{2}= 6^{2} - quadratic equation, for any given x if ax
^{2}+ bx + c =0 then x has 2 solutions

x=(-b+√(b^{2}- 4ac)/2a, x=(-b-√(b^{2}- 4ac)/2a - x
^{a}y^{b}is not equal to (xy)^{a+b} -
__Functions__f(x)= 9x + 5; where f is function of x (why? because it changes with x, it depends on x). value of f can be obtained by substituting x in '9x + 5', so f(2) =23 when x=2. The domain of any function is set of all permissible inputs values of the variable (in above case it's all permissible values of x).

for above inequality we need solutions for x.. above equation is equivalent to -3x < 18 or -x < 6 which means x > -6

hence x can be -5,-3.. 1,2... (infinite values)

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