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**Hint:**We have to solve the mathematical expression by cross multiplication method. For that we need to multiply the denominator of the right-hand side to the numerator of the left-hand side and opposite to the other side. And then will form a linear equation, and the value of x is found.

**Complete step by step solution:**

In the above question, we are given an expression

$\dfrac{{x - 1}}{{x + 1}} = \dfrac{7}{9}$ and we had to find the value for x.

So, doing cross multiplication

$9\left( {x - 1} \right) = 7\left( {x + 1} \right)$

Hence, multiplying into the brackets

$9x - 9x = 7x + 7$

Taking the variables to the left-hand side and constants to the right-hand side.

$9x - 7x = 7 + 9$

So, $2x = 16$

Finding the value of x by dividing both sides by $2$

$ \Rightarrow x = \dfrac{{16}}{2} = 8$

**Hence, the value of x is $8$**

**Note:**While taking the variables to the left-hand side or right-hand side sign will always change but not in the case for division. In the first step we are just going cross multiplication. But be careful while adding or subtracting where signs will change on changing the sides.

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