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 ⅓- 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 mid-point 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)/(-7-3) = 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}+3x-70=0

X(x+10)-7(x+10) = 0

(X+10)(X-7)=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

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