Solving Equations and Inequalities - Coursework Example

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WEEK 4 Chapter 2 pages 120 - 163 in your textbook.



The major difference between solving equations and solving inequalities is that when solving inequalities if the equation is multiplied by a number less than 0, the sign of inequality changes. The sign does not change when solving equations. For example, -x≥5 will become x≤-5.
When the inequality sign is greater than, the inequality sign has an open mouth ≥. This is how I remember which symbol is greater than and which one is less than.


Let x = no. of liters of a 10% acid solution
Acid in the solution= 0.1x + (0.25)(5)
= 0.1x + 1.25
Total liters of acid in solution= 0.15(x+5)
0.15x + 0.75=0.1x + 1.25
0.05x= 0.5
X=10
10 liters of 10% acid solution is required.


C. [ represents equal to and greater than means to the right of -4.

Let x= speed on a two-lane state road
Speed on freeway= x+25
3x+6(25+x)=510
3x+150+6x=510
9x=360
X=40
Speed on the freeway=40+25= 65 miles per hour

4-5x>11
-5x>7
X<-7/5

A)

The perimeter of a rectangle= 2L+2B
Length=x
Width=x-8
2x+2(x-8)=72
2x+2x-16=72
4x=88
X=22
Width=x-8
=22-8
=14 meters

24-(u/3)

19-7t≤-2
-7t≤-21
t≥3

19-7t>-9
-7t>-28
T<4
3≤t<4




Let invested Money = x
0.07x+0.14(2x)=1406.3
0.07x+0.28x=1406.3
0.35x=1406.3
X=$4018
Money invested = $4018 and $8036


X+x+1+x+2=240
3x+3=240
3x=237
X=79
3 consecutive numbers are 79, 80, and 81.
WEEK 5 Chapter 3 pages 169--217 in your textbook.


1) slope-intercept form (y=mx+c)
2) Point slope form (y-y_1=m(x-x_1 )
3) Equation of a vertical line (x=k)
4) Equation of a horizontal line (y=k)
5) General equation of a line (a x + b y = c)

Steps to graph the line:
Insert 5-6 values of x (x=-2. X=-1, x=0, x=1, x=2) in the equation of the line y= mx + c and find the corresponding y values. Once the points in the form (x,y) are obtained, mark them on the graph. Draw a straight line over the points plotted and extend the line.





x-intercept (y=0): 4x+0=-12
x= -3

y-intercept (x=0): 3y=-12
y= -4

Y=mx+c
4=1/5(10)+c
C=2
Y=1/5x+2

-9x+7y=-2
7y= 9x-2
Y=9/7x-2/7
Slope = 9/7
y-intercept= -2/7

Y=11+4
=15
(11,15)

46= 6x-14
6x=60
X=10
(10,46)

Y=(4x-3)/3
3y= 4x-3

(-2,2) and (-2,0)
M= (0-2)/(-2+2)
= -2/0
= ∞

(-2,1) and (-4,-2)
M= (-2-1)/(-4+2)
= -3/-2
=3/2

slope for line L= -1/m
= -2/3

(-11,11) and (-1,-7)
Slope= (-7-11)/(-1+11)
= -18/10
= -9/5

(-2,1) and (-4,-2)
M= (-2-1)/(-4+2)
= -3/-2
=3/2

slope for line L= -1/m
= -2/3
Y=mx+c
-2= (-2/3)(5)+c
C= 4/3
Y= -2/3x+4/3
3y= -2x+4


WEEK 6 Chapter 5 pages 297 - 354 in your textbook


FOIL does make it easier to multiply binomials. However, it is at a very basic level and once some practice is done, binomials can be multiplied intuitively and without memorizing the FOIL method. No, the order does not matter since any term can be multiplied first and the answer will not change even if the order is changed.


2 1 8 -7

1 2 20
1 10 13

Quotient= x+10
Remainder= 13

P(-1)= 1-(-1)+1-(-1)+1
=5

(7x(x^2+2x+8))/7x

= x^2+2x+8

Any number to the power of 0 is 1
Hence (-2pq)^0= 1

(U^12)(U^-72)
U^-60
= 1/u^60

8{〖(xy)〗^2}

B^4-7
= b^-3
1/b^3

10b^2+14b+45b+63
10b^2+59b+63


4z(z^16)/{(24z^5)(z^6)}
4(z^17)/(24(z^11))
z^6/6


(z^5)^2-(y)^2
z^10-y^2 Read More