Question

solve 2x+1/3x-2=59 and verify the answer.​

Answer 1

The value of x is $\dfrac{119}{115}$.

Step-by-step explanation:

Given, $\dfrac{2x+1}{3x-2}=59$ ... ... (1)

• Hint: Transpose (3x - 2) to the right hand side

⇒ 2x + 1 = 59 (3x - 2)

⇒ 2x + 1 = 177x - 118

⇒ 177x - 2x = 1 + 118

• Hint: Transposing x terms to one side and the numbers to the other side

⇒ 175x = 119

⇒ x = $\dfrac{119}{175}$

So, the value of x is $\dfrac{119}{175}$

Checking step:

Putting $x=\dfrac{119}{175}$ in LHS of (1), we get

LHS = $\dfrac{2\times\dfrac{119}{175}+1}{3\dfrac{119}{175}-2}$

= $\dfrac{\dfrac{238}{175}+1}{\dfrac{357}{175}-2}$

= $\dfrac{238+1\times 175}{357-2\times 175}$

= $\dfrac{413}{7}$

= 59 = RHS

So, the solution is verified.

#SPJ3

Answer 2

$\underline{\textbf{Given:}}$

$\mathsf{\dfrac{2x+1}{3x-2}=59}$

$\underline{\textbf{To find:}}$

$\textsf{The value of 'x' satisfying}\;\mathsf{\dfrac{2x+1}{3x-2}=59}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{2x+1}{3x-2}=59}$

$\textsf{This can be written as,}$

$\mathsf{2x+1=59(3x-2)}$

$\mathsf{2x+1=177\,x-118}$

$\textsf{Rearranging terms, we get}$

$\mathsf{177\,x-2\,x=118+1}$

$\mathsf{175\,x=118+1}$

$\mathsf{x=\dfrac{119}{175}}$

$\implies\boxed{\mathsf{x=\dfrac{17}{25}}}\;\;\;\mathsf{(\because\,reduced\;by\;7)}$

$\underline{\textbf{Verification:}}$

$\mathsf{L.H.S}$

$\mathsf{=\dfrac{2x+1}{3x-2}}$

$\mathsf{=\dfrac{2\left(\dfrac{17}{25}\right)+1}{3\left(\dfrac{17}{25}\right)-2}}$

$\mathsf{=\dfrac{\dfrac{34}{25}+1}{\dfrac{51}{25}-2}}$

$\mathsf{=\dfrac{\dfrac{34+25}{25}}{\dfrac{51-50}{25}}}$

$\mathsf{=\dfrac{\dfrac{59}{25}}{\dfrac{1}{25}}}$

$\mathsf{=59}$

$\mathsf{=R.H.S}$