Solving Inequalities, Limits and Derivatives

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MATH 30102 - CALCULUS & ANALYTIC GEOMETRY (Thomas)

Solve the following inequalities/equations expressing the solution. Show all work and box the final answer.
1) 5x - 3 7 - 3x
Rearragne the equation so that items with x on the left side, and the constants are the right side.

The solution is
2) 3 - < ½
First, the abosolute can be rewritten as
For ,
(1)
For
(2)
x satisfy the above equation, that is (3)
The reason I ddin't solve the inequailities (1) and (2) seperately is that you have to analyze the cases of x>0 and x<0 seperately.
With (3), it is obvious that x>0. Given x>0
When
(4)
When
(5)
So the solution is

3) ( x - 1 ) 2 < 4

There are two cases: (1)
, which is impossible.
(2)

The solution is

Write an equation for the line described below.

4) Passes through ( -1, 1 ) with solpe -1
Assume the equation of the line is . We know the slope is m=-1, so the equation is . Now the line is throught (-1, 1), so substitute into the line equation,

So the line equatin is

5) A particle starts at A ( -2, 3 ) and its coordinates change by increments x = 5,

y = - 6. Find its new position.
The starting x-position is , so

The starting y-position is , so

Sot the ...