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Solution:

(4x

= 4x

= 4x

= 9x

= 3x(3x + 2).

Solution:

(-7x

= -7x

= -7x

= -11x

= -x(11x + 2)

Solution:

(-5x

= -5x

= -5x

= -10x

Solution:

(4x

= 4x

= 4x

= 5x

= 5x

Solution:

(-6x + 3) - (-x

= -6x + 3 + x

= -6x - 5x + x

= x

Solution:

(-9x - 5) - (-9x

= -9x - 5 + 9x

= 9x

= 9x

= x(9x – 10)

**7. Simplify: (2x - 4) - (6x + 6)
Solution:**

(2x - 4) - (6x + 6)

= 2x - 4 - 6x – 6

= 2x – 6x – 4 – 6

= -4x – 10

= -2(2x + 5)

Solution:

(8+4x)/4x

= 4(2 + x)/4x

[Cancel 4 from the numerator and denominator]

= (2 + x)/x

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

Solution:

3x – 5 + 23x – 9

= 3x + 23x – 5 – 9

= 26x – 14

= 2(13x – 7)

(a) One real root (a double root),

(b) Two distinct real roots,

(c) Three real roots,

(d) None (two imaginary roots)

Solution:

Discriminant = bx

Compare the above equation 3x

We get, a = 3, b = -5, c = 1

Put the value of a, b and c;

Discriminant = bx

Discriminant = (-5)

= 25 – 12

= 13 [13 > 0]

Therefore, discriminant is positive.

So the given equation has two distinct real roots.

(a) One real root (a double root),

(b) Two distinct real roots,

(c) Three real roots,

(d) None (two imaginary roots)

Solution:

Discriminant = b

Compare the above equation 7x

We get, a = 7, b = 3, c = 1

Put the value of a, b and c;

Discriminant = b

Discriminant = (3)

= 9 – 28

= -19 [13 < 0]

Therefore, discriminant is negative.

So the given equation has none (two imaginary roots).

**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) ---------

(b) (-4, -2) ---------

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