Question

If (4x + 5): (3x +11) = 13:17. find the value of x
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Answer 1

$\huge{\bigstar}$$\boxed{\huge{\red{\mathfrak{Answer}}}}$$\huge{\bigstar}$

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→$\frac{(4x+5)}{(3x+11)} = \frac{13}{17}$

→$13(3x+11) = 17(4x+5)$

→$39x + 143 = 68x + 85$

→$29x = 58$

$\huge{x = 2}$

Answer 2

Given :-

$= \texttt{(4}x \: \: \texttt{+ 5) : (3}x \: \: \texttt{+ 11) = 13} : \texttt{17}$

This can be written as :-

$= \frac{\texttt{(4}x\texttt{ + 5)}}{\texttt{(3}x\texttt{ + 11)}} \: = \: \frac{\texttt{13}}{\texttt{17}}$

Now let us solve the above mentioned equation :-

$= \frac{\texttt{(4}x\texttt{ + 5)}}{\texttt{(3}x \texttt{ \: + 11)}} = \frac{13}{17}$

$=\texttt{17×( 4}x\texttt{ + 5) \: = \: 13}×\texttt{(3}x \texttt{ + 11) }$

$= \texttt{17(4}x\texttt{ + 5) = 13(3}x\texttt{ + 11)}$

$= \texttt{68}x \texttt{ \: + \: 85 = 39}x \texttt{ \: + \: 143}$

$=\texttt{ 68}x\texttt{ - 39}x \texttt{ \: = \: 143 - 185}$

$= \texttt{29}x \texttt{ \: = \: 143 - 85}$

$= \texttt{29}x \texttt{ \: = \: 58}$

$= x \: \texttt{ = } \: \frac{\texttt{58}}{\texttt{29} }$

$=\color{hotpink} x \texttt{ \: = \: 2}$

Let us check whether or not we have found out the correct value of x, by placing 2 in the place of x :-

$= \frac{\texttt{ (4 × 2 + 5)}}{\texttt{(3 × 2 + 11)}} = \frac{\texttt{13}}{\texttt{17} }$

$= \frac{\texttt{(8 + 5)}}{\texttt{(6 + 11)}} = \frac{\texttt{13}}{\texttt{17} }$

$= \frac{\texttt{13}}{\texttt{17}} \texttt{ \: = \: } \frac{\texttt{13}}{\texttt{17}}$

$\color{orage}\hookrightarrow \texttt{\color{olive}LHS = \color{hotpink}RHS }</p><p>$

As the left hand side of the equation is equivalent to the right hand side of the equation, we can conclude that we have found out the correct value of x .

Therefore, the value of x = 2

the value of x = 2