What is the value of x in the given equation- 3x-1 - 16 - 2x-3 - 7 - x-3 - 8 - 3x-1 - 14

The correct option is B 5 Given, 3x+116+2x 37=x+38+3x 114 .Taking LCM on both sides, we get,LCM of 16,7= LCM of 8,14=112 .Then, #16 ...

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Byju's Answer

Standard XII

Mathematics

Logarithms

What is the v...

Question

What is the value of $x$ in the given equation?
$\frac{(3 x + 1)}{16} + \frac{(2 x - 3)}{7} = \frac{(x + 3)}{8} + \frac{(3 x - 1)}{14}$

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Solution

The correct option is B $5$
Given,
$\frac{3 x + 1}{16} + \frac{2 x - 3}{7} = \frac{x + 3}{8} + \frac{3 x - 1}{14}$ .

Taking LCM on both sides, we get,
LCM of $16, 7 =$ LCM of $8, 14 = 112$ .

Then,
$⟹$ $(\frac{3 x + 1}{16} \times \frac{112}{112}) + (\frac{2 x - 3}{7} \times \frac{112}{112}) = (\frac{x + 3}{8} \times \frac{112}{112}) + (\frac{3 x - 1}{14} \times \frac{112}{112})$

$⟹$ $\frac{7 (3 x + 1)}{112} + \frac{16 (2 x - 3)}{112} = \frac{14 (x + 3)}{112} + \frac{8 (3 x - 1)}{112}$

$⟹$ $\frac{7 (3 x + 1) + 16 (2 x - 3)}{112} = \frac{14 (x + 3) + 8 (3 x - 1)}{112}$ .

Now, cancelling $112$ from both sides, we get,

$⟹$ $7 (3 x + 1) + 16 (2 x - 3) = 14 (x + 3) + 8 (3 x - 1)$

$⟹$ $21 x + 7 + 32 x - 48 = 14 x + 42 + 24 x - 8$

$⟹$ $21 x + 32 x - 14 x - 24 x = 42 - 8 - 7 + 48$

$⟹$ $15 x = 75$

$⟹$ $x = 5$ .

Therefore, option $D$ is correct.

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Similar questions

Q. Solve for

x : \frac{(3 x + 1)}{16} + \frac{(2 x - 3)}{7} = \frac{(x + 3)}{8} + \frac{(3 x - 1)}{14}

Solve each of the following equations and also verify your solution :

$\frac{(3 x + 1)}{16} + \frac{(2 x - 3)}{7} = \frac{(x + 3)}{8} + \frac{(3 x - 1)}{14}$

Statement 1: The value of the polynomial ${x}^{5}+ 2{x}^{4}+ 3{x}^{3}+ {x}^{2}– 7x + 8$ at x = -1 is 14.

Statement 2: The polynomial ${x}^{5}+ 2{x}^{4}+ 3{x}^{3}+ {x}^{2}– 7x + 8$ when divided by x + 1, gives 14 as remainder.

Solve :

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

Q. If the value of

x

satisfying the equation

(\frac{1 - 2 x}{7}) - (\frac{2 - 3 x}{8}) = \frac{3}{2} + \frac{x}{4}

- m

.Find

m

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What is the value of x in the given equation?(3x+1)16+(2x−3)7=(x+3)8+(3x−1)14

What is the value of $x$ in the given equation?
$\frac{(3 x + 1)}{16} + \frac{(2 x - 3)}{7} = \frac{(x + 3)}{8} + \frac{(3 x - 1)}{14}$