Question

Solve
$5x \: + \frac{7}{2} = \frac{3}{2}x \: - 14$
।
★ Answer correctly... Don't spam.


​

Answer 1

Answer :-

$\sf5x + \dfrac{7}{2} = \dfrac{3}{2}x - 14$

The LCM of 1 and 2 is 2, 5x/1 and 7/2 using their denominators,

$\sf \dfrac{5x \times 2 + 7 \times 1}{2} = \dfrac{3}{2}x - 14$

On simplifying,

$\sf\dfrac{10x + 7}{2} = \dfrac{3}{2}x - 14$

Now, the LCM of 1 and 2 is 2, so subtracting 3x/2 and 14/1 using their denominators,

$\sf \dfrac{10x + 7}{2} = \dfrac{3x \times 1 - 14 \times 2}{2}$

On simplifying,

$\sf \dfrac{10x + 7}{2} = \dfrac{3x - 28}{2}$

By cross multiplication,

$\sf2 \: (10x + 7) = 2 \: (3x - 28)$

Removing the brackets,

$\sf20x + 14 = 6x - 56$

Transposing 14 from LHS to RHS, changing it's sign,

$\sf20x = 6x - 56 - 14$

Subtracting 14 from -56,

$\sf20x = 6x - 70$

Transposing 6x from RHS to LHS, changing it's sign,

$\sf20x - 6x = - 70$

Subtracting 6x from 20x,

$\sf14x = - 70$

Transposing 14 from LHS to RHS, changing it's sign,

$\sf x = \dfrac{ - 70}{ \: \: \: 14}$

Dividing -70 by 14,

$\underline{ \boxed{ \sf x = - 5}}$

• The value of x is -5.

-----------------------------------------------------------

V E R I F I C A T I O N

To check our answer, let's put 5 in the place of x and see whether LHS = RHS.

LHS

$\rm5x + \dfrac{7}{2}$

Substituting the value of x,

$\rm5 \times ( - 5) + \dfrac{7}{2}$

Applying the BODMAS rule and multiplying 5 with -5,

$\rm( - 25) + \dfrac{7}{2}$

The LCM of 1 and 2 is 2, so adding the fractions using their denominators,

$\rm\dfrac{( - 25) \times 2 + 7 \times 1}{2}$

On simplifying,

$\rm\dfrac{ (- 50) + 7}{2}$

Adding 7 to -50,

$\rm\dfrac{( - 43)}{2}$

RHS

$\rm\dfrac{3}{2} x - 14$

Substituting the value of x,

$\rm\dfrac{3}{2} \times ( - 5) - 14$

Applying the BODMAS rule and multiplying 3/2 with -5,

$\dfrac{( - 15)}{2} - 14$

The LCM of 2 and 1 is 2, so subtracting the fractions using their denominators,

$\dfrac{( - 15) \times 1 - 14 \times 2}{2}$

On simplifying,

$\rm\dfrac{( - 15) - 28}{2}$

Subtracting 28 from -15,

$\rm \dfrac{( - 43)}{2}$

-----------------------------------------------------------

LHS = RHS.

Hence verified!

Answer 2

$\huge\mathfrak\color{navy}{ \underline{ \color{navy}{★ \:Solution:-}}}$

$5x \: + \frac{7}{2} = \frac{3}{2}x \: - 14$

By transforming numbers to LHS and RHS,

$\frac{7}{2} + 14 = \frac{3x}{2} - 5x$

By adding the constants and variables,

$\frac{7 + 28}{2} = \frac{3x - 10x}{2}$

By calculating the values,

$\frac{35}{2} = \frac{ - 7x}{2}$

By transforming 2 to RHS,

$35 = \frac{ - 7}{2} \times 2$

By Cancelling 2 from RHS.

$35 = - 7x$

Transforming-7 to other side,

$x = \frac{35}{ - 7}$

By calculating,

$x = - 5$

Hence, x=-5