W.i.p 4
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1. 3x </= 3(x + 12)
=>3x </= 3x + 36
=> 36 >/= 0
Which is an improbability
Hence the solution set is phi
2. 3x + 10 > 3(x + 8)
=>3x + 10 > 3x + 24
=> 14 < 0 which is an improbability
Hence the solution set is phi
3. 11 – 3(3 - x) </= 23
=>11 – 9 + 3x </= 23
=> 3x </= 23 – 11 + 9
=> 3x </= 21
=> x </= 7
Hence the solution set of the given equation is ( -- infinity, 7]
y + 2 = 0
=>y = -2
Hence the graph of the given equation is
Y|
|
|
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-X<----------(-|2)-----------(-1)---------|-----------(1)------------(2)----X
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(-1)|
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Y = -2 |
<------------------------------------------(-2)-------------------------------------
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-Y
4. Determine whether the ordered pair is the solution of the given equation:
(-2, -2)
Y = X + 4
Putting the values x = -2 and y = -2 in the given equation we get
-2 = -2 + 4
=> -2 = 2 which is not true
Hence the given ordered pair is not a solution set of the given equation.
5. 3 </= x < 7
Solution set is [3, 7)
6. x – 2y = 2
Putting x = 0 in the given equation, we have
0 – 2y = 2
=>-2y = 2
=> -2y/2 = 2/2
=> -y = 1
=> y = -1
When y = 0, x – 2(0) = 2
=>x – 0 = 2
=> x = 2
Hence the y and x axes intercepts of the equation is (0, -1) and (2, 0)
6. 8> y = -x + 4
For x = 0, y = 0 + 4 = 4
For y = 0, 0 = -x + 4
=>x = 4
Hence, the solution set (0, 4) and (4, 0)
7. Let mark scored on the fifth test be x to have overall test score of at least 83
So (x + 85 + 87 + 88 + 75)/5 = 83
=>x + 335 = 83 X 5 = 415
=> x = 415 – 335 = 80
Hence Claire must score 80 in her last test to get an average total score of 83.
8. If (x1, y1) and (x2, y2) are the coordinates of any two points on a line, then its slope is
m = (y2 – y1)/(x2 – x1)
In the given problem, slope m = [10 – (-10)]/(15 - 17) = 20/(-2) = -20/2 = -10
9. Any line parallel to y = -4x -1 has its slope m = -4
Hence, equation of the line is y = -4x + c
Since, it passes through (2, 6)
Therefore, 6 = -4(2) + c
=>c = 6 + 8 = 14
Hence, the required equation is y = -4x + 14
10. slope of the given line is m = (1 – 0)/(-4) = -1/4
11. Since, line is parallel to y-axis, therefore, slope is undefined
12. Here, slope m = -1/5 and intercept c = 2
Since, slope is negative and intercept is 2
13. 2x + 4y = 8
=>4y = -2x + 8
=> y = -1/2 x + 2
Here, slope m = -1/2 and c = 2
14. m1 = (17 – 3)/[(-5) – (-3)] = 14/(-2) = -7
m2 = (2 - 3)/(6 – 13) = (-1)/(-7) = 1/7
m1 X m2 = (-7) X (1/7) = -1
Hence, the lines are perpendicular
15. 9x + y = 3
=>y = -9x + 3
Intercept c = -9
16. Thee required equation is y – 6 = (1 - 6)/(4 - 8)(x - 8)
=>y – 6 = (-5)/(-4)(x - 8)
=> y – 6 = 5/4(x - 8)
=> y = 5/4x – 10 + 6
=> y = 5/4x – 4
17. Equation of line passing through (-5, 2) and slope = 6 is
2 = 6 X (-5) +c
=>c = 2 + 30 = 32
Hence, y = 6x + 32
18. Here the two coordinates are (5, 69) and (1,169)
Hence, the required equation is y – 69 = (169 - 69)/(1 - 5)(x - 5)
=>y – 69 = 100/(-4) (x - 5)
=> y – 69 = -25x + 125
=> y = -25x + 194
19. x + y > -1
20. -2x -4y ≤ 8
=>y ≤ -1/2 x- 2
Slope = -1/2 and intercept = -2
