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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)
13. Fill in the blank:
(a) The point with coordinates (0,0) is called ........of a rectangular coordinate system.
(b) To find the x-intercept of a line, we let....equal 0 and solve for
......; to find y-intercept, 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 x-intercept of a line, we let y equal 0 and solve for x ; to find y-intercept, we let x equal 0 and solve for y .
14. 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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