Question

Solve the following equation: \[5x-(4x-7)(3x-5)=63(4x-9)(x-1)\]

Answer 1

Hint: First, we will multiply the terms in the brackets on both the sides. Next, open the brackets on both the sides and change the sign of all the terms which were within brackets. Cancel the common term: \[-12{{x}^{2}}\]. Simplify the expression and solve for x to get the final answer.

Complete step-by-step answer:

In this question, we need to solve the equation: \[5x-(4x-7)(3x-5)=63(4x-9)(x-1)\]

First, we will multiply the terms in the brackets on both the sides.

\[5x-(12{{x}^{2}}-20x-21x+35)=6-3(4{{x}^{2}}-4x-9x+9)\]

\[5x-(12{{x}^{2}}-41x+35)=6-3(4{{x}^{2}}-13x+9)\]

Now, we will open the brackets. While opening the brackets, the signs of all the terms in the brackets will change because both the brackets are being subtracted to some number. On opening the brackets, we will get the following:

\[5x-12{{x}^{2}}+41x-35=6-12{{x}^{2}}+39x-27\]

We see that the term \[-12{{x}^{2}}\] is common on both the sides. So, we will cancel this term. On cancelling this term and simplifying the rest of the expression, we will get the following:

$\Rightarrow$ \[46x-35=39x-21\]

$\Rightarrow$ \[46x-39x=35-21\]

$\Rightarrow$ \[7x=14\]

$\Rightarrow$ \[x=2\]

Hence, \[x=2\] is the final answer.

Note: In this question, it is very important to solve each step in the simplification carefully. This question involves very lengthy calculations and some students might make mistakes while doing simplification which need to be avoided. Also, note that while opening the brackets, the signs of all the terms in the brackets will change because both the brackets are being subtracted to some number.