Question

Solve:
 $ 3\left( {5x - 7} \right) - 2\left( {9x - 11} \right) = 4\left( {8x - 13} \right) - 17 $

Answer 1

Hint: To find value or solution of this type of equation. We first simplify or solve brackets on both sides left as well as right and then shifting ‘x’ variable terms on one side and other equations on the other side. Then adding or subtracting like terms according to sign of terms and so value of ‘x’ and hence solution of given problem.

Complete step-by-step answer:
Given equation is
 $ 3\left( {5x - 7} \right) - 2\left( {9x - 11} \right) = 4\left( {8x - 13} \right) - 17 $
To solve the above written equation. We first open brackets given on both sides and then shifting x variables terms on one side and other on the other side. Then adding or subtracting like terms and so to get the value of x.
Simplifying the given equation. We have
 $
  3\left( {5x - 7} \right) - 2\left( {9x - 11} \right) = 4\left( {8x - 13} \right) - 17 \\
   \Rightarrow 15x - 21 - 18x + 22 = 32x - 52 - 17 \\
   \Rightarrow 15x - 18x - 32x = - 52 - 17 + 21 - 22 \\
   \Rightarrow - 3x - 32x = - 69 - 1 \\
   \Rightarrow - 35x = - 70 \\
   \Rightarrow x = \dfrac{{ - 70}}{{ - 35}} \\
   \Rightarrow x = \dfrac{{70}}{{35}} \\
   = 2 \;
  $
Therefore, the required value of the given linear equation is $ 2. $
So, the correct answer is “2”.

Note: For this type of problem while having brackets. So one should open or simplify brackets carefully as if there is a negative sign outside as a multiple then each term inside the bracket will have a change in sign after multiplication. So, one should do this step carefully as any silly mistake of change in sign will lead to wrong answers and so wrong solutions to the given problem.