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|4x+3|>1
set absolute value of |4x+3|>1 to -4x+3 >1and 4x+3>1 and solve for x. there will be 2 answers.
x=2+√(x2-1)
Isolate the square root by subtracting two on both sides and squaring both sides. (Need to check this problem since you squared both sides-the answer might not be a solution)
x-2
----- ≥ 0
x+2
Draw a chart that will tell you where the left hand side is greater or equal to zero. The chart should look like this:
(-∞,-2) (-2,2) (2,∞)
x-2              -          -          +
x+2             -           +         +
x-2/x+2       +           -          +

LHS is ≥0 at the interval (-∞,-2) and (2,∞).
(1/x)2 + 4 = 5(1/x)
substitute w=1/x and solve for w.
w2+4=5w
(You need to remember to put 1/x back into the equation after you solve)
Let A = (2,-3) and B = (-7,5)
(a) find the midpoint between A and B
(b) find the point 1/4 of the way from A to B.
(c) Find the point 1/8 of the way from A to B.
Use the midpoint formula to solve (a). Then take the A coordinates (2,-3) and the coordinates from problem (a) and do the midpoint formula again to get the answer for (b). Then take the A coordinates (2,-3) and the coordinates from problem (b) and use the midpoint formula again.
Sketch a graph of x2+y2=6x+12y+36
You need to get the x and y coordinates on one side and then complete the square for both the x and the Y coordinate. The final answer should be in the equation of a circle-(x-h)2+(y-k)2=r2
(when you complete you square don't forget to add to both sides of the equation)
Graph the piecewise function ƒ define by:
------|(x-3)2 when 4<x
ƒ(x)=|2   when 2<x≤4
------|(x-3)2 when x≤2
what is the range of ƒ?
You can graph this on your graphing calculator.

Your range is [1,∞]
Suppose we need to describe a square using equations. The line segment from (1,1) to (2,3) is one edge of the square. Find the equations of the four lines which forms the sides of the square.
Find line 1 by finding the slope (y2-y1)/(x2-x1) and putting it into point slope form.
Find line 2 by finding the slope of a line that is perpendicular to line 1 which would be the inverse of the first slope. Put that into point slope form.
Find line 3 by finding the line through points (2,3) and with a slope -1/2. Put that into point slope form.
Find line 4- along line 1 there is a rise of 2 and a run of 1. Along line 2 there is there is a drop of 1 and a run of 2. So (-1,2) lies on line 4. Put into point slope form.
Solve for x, and check your work

x2-5x+4=0
Un FOIL the problem and set both x's equal to zero and solve for x.
Find all real solutions of x2+3x+1=0
Insert this problem into the quadratic formula and then simplify.
Express the following phrase as an inequality involving an absolute value: the set of real numbers a distance of 7 or less from the number 3.
|3-x|≤7 or |x-3|≤7
Solve for x: (x-4)4+4=5(x-4)2
Let w=(x-4)

w4+4=5w2

(remember to put (x-4) back into the problem once you solve)

(x-4)
-----------≥ 0
(x-2)(x-6)
Create a table from (-∞,2)(2,4)(4,6)(6,∞) to see where the left hand side changes sign.

Answer should be in interval notation (2,4]υ(6,∞)
Solve for x: |2x+3|≥5
solve absolute value by solving -
2x+3≥5  and -(2x+3)≥5
x of y cards