X-3-2-3 x-1-4-2x-2-3-2

X + 3/2 3x + 1/4 = 2 (x 2)/3 2 2 (x + 3) (3x + 1)/4 = 2 (x 2) 6/3 2x + 6 3x 1/4 = 2x 4 6/3 x + 5/4 = 2x 10/3 3x + 15 = 8x 40 55 = 1 ...

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Byju's Answer

Standard VIII

Mathematics

Solving Linear Equations Using Transpose of Terms

x+3/2-3 x+1/4...

Question

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

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Solution

$\frac{x + 3}{2} - \frac{3 x + 1}{4} = \frac{2 (x - 2)}{3} - 2 \frac{2 (x + 3) - (3 x + 1)}{4} = \frac{2 (x - 2) - 6}{3} \frac{2 x + 6 - 3 x - 1}{4} = \frac{2 x - 4 - 6}{3} \frac{- x + 5}{4} = \frac{2 x - 10}{3} - 3 x + 15 = 8 x - 40 55 = 11 x S o, x = \frac{55}{11} = 5$

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Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

$\frac{(2 x - 1)}{3} \geq \frac{(3 x - 2)}{3} \geq \frac{(3 x - 2)}{4} - \frac{(2 - x)}{5}$

Q. Solve the equations:

\frac{3 x^{4} + x^{2} - 2 x - 3}{3 x^{4} - x^{2} + 2 x + 3} = \frac{5 x^{4} + 2 x^{2} - 7 x + 3}{5 x^{4} - 2 x^{2} + 7 x - 3}

Q. Let

p (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 3 & 3 x & 3 x^{2} + 2 3 x & 3 x^{2} + 2 & 3 x^{3} + 6 x 3 x^{2} + 2 & 3 x^{3} + 6 x & 3 x^{4} + 12 x^{2} + 2 \end{matrix} ∣ ∣ ∣ ∣ ∣

q (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 2 & 2 & 2 2 + x & 3 + x & 4 + x (2 + x)^{2} & (3 + x)^{2} & (4 + x)^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

r (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} cos (x + π / 4) & sin (x + π / 4) & 1 cos (x + π / 2) & sin (x + π / 2) & \sqrt{2} cos (x + 3 π / 4) & sin (x + 3 π / 4) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

s (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 x & 2 x + 1 4 x & 2 x (2 x - 1) & 2 x (2 x + 1) 6 x (2 x - 1) & 4 x (2 x - 1) (x - 1) & 2 x (4 x^{2} - 1) \end{matrix} ∣ ∣ ∣ ∣ ∣

Match the expressions on the left with their properties or values on the right.

Q. Solve:

lim x \to - 2 \frac{x^{4} + 2 x^{3} + 3 x^{2} + 5 x - 2}{x^{5} + 3 x^{4} + 2 x^{3} + 3 x^{2} + 7 x + 2}

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(x+3)2−(3x+1)4=2(x−2)3−2

x+32−3x+14=2(x−2)3−22(x+3)−(3x+1)4=2(x−2)−632x+6−3x−14=2x−4−63−x+54=2x−103−3x+15=8x−4055=11xSo,x=5511=5

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

$\frac{x + 3}{2} - \frac{3 x + 1}{4} = \frac{2 (x - 2)}{3} - 2 \frac{2 (x + 3) - (3 x + 1)}{4} = \frac{2 (x - 2) - 6}{3} \frac{2 x + 6 - 3 x - 1}{4} = \frac{2 x - 4 - 6}{3} \frac{- x + 5}{4} = \frac{2 x - 10}{3} - 3 x + 15 = 8 x - 40 55 = 11 x S o, x = \frac{55}{11} = 5$