Question 67Solve the following-3x-x-2-3-4-x-1-4

Given, 3x x 2/3=4 x 1/4 ⇒9x (x 2)/3=16 (x 1)/4 ⇒ 4(9x x+2)=3(16 x+1) ⇒ 4(8x+2)=3( x+17) ⇒ 32x+8= 3x+51 ⇒ 32x+3x=51 8 ⇒ 35x=43 ⇒35x/35=43/35 ∴ x=43/35 ...

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Standard VI

Mathematics

Solution of an Equation

Question 67So...

Question

Question 67

Solve the following:

$3 x - \frac{x - 2}{3} = 4 - \frac{x - 1}{4}$

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Solution

Given, $3 x - \frac{x - 2}{3} = 4 - \frac{x - 1}{4} \Rightarrow \frac{9 x - (x - 2)}{3} = \frac{16 - (x - 1)}{4} \Rightarrow 4 (9 x - x + 2) = 3 (16 - x + 1) \Rightarrow 4 (8 x + 2) = 3 (- x + 17) \Rightarrow 32 x + 8 = - 3 x + 51 \Rightarrow 32 x + 3 x = 51 - 8 \Rightarrow 35 x = 43 \Rightarrow \frac{35 x}{35} = \frac{43}{35} ∴ x = \frac{43}{35}$

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Question 67

Solve the following:

$3 x - \frac{x - 2}{3} = 4 - \frac{x - 1}{4}$

Q. Question 1
Determine which of the following polynomials has (x+1) a factor:
(i)

x^{3} + x^{2} + x + 1

(ii)

x^{4} + x^{3} + x^{2} + x + 1

(iii)

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

(iv)

x^{3} - x^{2} - (2 + \sqrt{2}) x + \sqrt{2}

Q. Question 13
x + 1 is a factor of the polynomial

A)

x^{3} + x^{2} - x + 1

x^{3} + x^{2} + x + 1

x^{4} + x^{3} + x^{2} + 1

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

Q. Solve the following equations:
a)

5 (3 - x) - 2 (4 - 3 x) = 11 - 2 (x - 1)

6 - 4 (x + 3) = 2 (x - 1)

5 (1 - 2 x) + 2 (3 - x) = 3 (x + 4) + 14

Question 24
Factorise
(i) $2 x^{3} - 3 x^{2} - 17 x + 30$

(ii) $x^{3} - 6 x^{2} + 11 x - 6$

(iii) $x^{3} + x^{2} - 4 x - 4$

(iv) $3 x^{3} - x^{2} - 3 x + 1$

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Solution of an Equation

Standard VI Mathematics

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Question 67 Solve the following: 3x−x−23=4−x−14

Given, 3x−x−23=4−x−14⇒9x−(x−2)3=16−(x−1)4⇒4(9x−x+2)=3(16−x+1)⇒4(8x+2)=3(−x+17)⇒32x+8=−3x+51⇒32x+3x=51−8⇒35x=43⇒35x35=4335∴x=4335

Question 67

Solve the following:

$3 x - \frac{x - 2}{3} = 4 - \frac{x - 1}{4}$