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7. Simplify: (2x  4)  (6x + 6)
Solution:
(2x  4)  (6x + 6)
= 2x  4  6x – 6
= 2x – 6x – 4 – 6
= 4x – 10
= 2(2x + 5)
Answer: 2(2x + 5)
8. Simplify:(8+4x)/4x
Solution:
(8+4x)/4x
= 4(2 + x)/4x
[Cancel 4 from the numerator and denominator]
= (2 + x)/x
Answer: (2 + x)/x
9. Decide whether the lines are parallel, perpendicular or neither.
x + 4y = 7 and 4x – y = 3
Solution:
x + 4y = 7
4y = x + 7
y = (1/4) x + 7
Slope of the equation x + 4y = 7 is 1/4.
Again, 4x – y = 3
y = 4x – 3
Slope of the equation 4x – y = 3 is 4.
Since multiplying both the slope of the equation = 1/4 × 4
= 1
Therefore, the given two equations are perpendicular to each other.
Answer: Perpendicular
10. Simplify: 3x – 5 + 23x – 9
Solution:
3x – 5 + 23x – 9
= 3x + 23x – 5 – 9
= 26x – 14
= 2(13x – 7)
Answer: 2(13x – 7)
11. A plane flies 420 miles with the wind and 350 miles against the
wind in the same length of time. If the speed of the wind is 23 mph,
what is the speed of the plain in still air?
Solution:
The speed of the plane in still air = x miles/hour
The speed of the wind is 23 mph
Speed with the wind = (x + 23) mph
Speed against the wind = (x – 23) mph
Time = Distance/ Speed
According to the problem,
420/(x + 23) = 350/(x – 23)
420(x – 23) = 350(x + 23)
420x – 9660 = 350x + 805
420x – 350x = 8050 + 9660
70x = 17710
x = 17710/70
x = 253
Therefore, the speed of the plane in still air = 253 mph.
14. Fill in the blank:
(a) The point with coordinates (0,0) is called ........of a rectangular coordinate system.
(b) To find the xintercept of a line, we let....equal 0 and solve for
......; to find yintercept, we let ......equal 0 and solve for.......
Solution:
(a) The point with coordinates (0,0) is called origin of a rectangular coordinate system.
(b) To find the xintercept of a line, we let y equal 0 and solve for x ; to find yintercept, we let x equal 0 and solve for y .
15. Name the quadrant, if any, in which each point is located.
(a) (1, 6)
(b) (4, 2)
Solution:
(a) (1, 6)  I Quadrant.
(b) (4, 2)  III Quadrant.
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