
Solve the following inequalities
3 – 2x < 5
4 – 3x >  8.
starting with the first part of the inequality, 3  2x < 5
When we take 3 to the other side, we get 2x < 2
Divide both sides by 2 (dividing by a negative number changes the inequality sign.)
Therefore we get x > 1
For the second part, 4  3x > 8
Taking 4 to the other side 3x > 4
Dividing both sides by 3 x < 1 1/3
Therefore our inequalities become 1 < x < 1 â  Determine the quartile deviation of the following data 4,9,5,4,7,6,2,1,6,7,8,3.
Quartile deviation = (upper quartile  lower quartile
To get the quartiles, we first arrange the data in ascending order
1, 2, 3, 4, 4, 5, 6, 6, 7, 7,8,9
Lower quartile = (3 +4)/2 = 3.5
Upper quartile = (7 + 7)/2 = 7
Quartile deviation is therefore (7  3.5)/2 = 1.75

Find the equation of the perpendicular line that passes through the mid – point X of C(  7 , 8) and D ( 3 ,  8)
To get the equation of a line, we have to determine the point at which it passes
We have been given a hint that it is the mid point of the line C(7 ,8) and D(3, 8)
To get the midpoint We take ((x1 + x2)/2 + (y1+y2)/2)
= (( 7 + 3)/2 , (8 + 8)/2) = (2,0)
Something else we know is that gradient of perpendicular lines are negative
So first we get the gradient of this line, which is change in y/ change in x
= (8  8)/(73) = 16/10
To find the equation, we apply this formulay  y1 = m(x  x1), where m is the gradient
y = 0 +16/10( x  2)
y = 16/10x  16/5
5y = 8x 16  The base of a triangle is 3cm longer than its height. Given that the area of the triangle is 35cm2, determine the height of the triangle.
We know that the area of a triangle = 1/2(b x h)
Let's assume height = x
Base becomes x + 3
Therefore area of the triangle1/2((x(x + 3)) = 35
X^{2}+3x70=0
X(x+10)7(x+10) = 0
(X+10)(X7)=0
X =10 or x=7
:HEIGHT = 7cm 
A certain two – digit number is equivalent to five times the sum of the digits. It is found to be 9 less than the number formed when the digits are interchanged. Find the number
Let x be the 10's digit and let y be the ones digit.
10x + y = 5 (x + y)
10x + y = (10y + x)  95x  4y = 0
9x  9y = 9