Question

Find the value of x. $3\left( {5x - 7} \right) - 2\left( {9x - 11} \right) = 4\left( {8x - 13} \right) - 17$.

Answer 1

Hint: To find the value of x in $3\left( {5x - 7} \right) - 2\left( {9x - 11} \right) = 4\left( {8x - 13} \right) - 17$, first of all write down the equation. Now open the brackets on both LHS and RHS. Now, gather all the x terms on LHS and all the constants on RHS. Now, carry out addition and subtraction and you will get the value of x.

Complete step-by-step answer:
In this question, we are given an equation in terms of x and we need to solve it and find the value of x.
Given equation: $3\left( {5x - 7} \right) - 2\left( {9x - 11} \right) = 4\left( {8x - 13} \right) - 17$
First of all, let us understand what an equation is.
An equation is a statement that two mathematical expressions are equal in values. That is left hand side is equal to right hand side.
Here, our LHS is $3\left( {5x - 7} \right) - 2\left( {9x - 11} \right)$ and the RHS is $4\left( {8x - 13} \right) - 17$.
Here, we have to solve $3\left( {5x - 7} \right) - 2\left( {9x - 11} \right) = 4\left( {8x - 13} \right) - 17$ and find the value of x.
First of all, open all the brackets on both LHS and RHS.
$ \to 15x - 21 - 18x + 22 = 32x - 52 - 17$
Now, gather all the x terms on LHS and all the constant terms on the RHS. Therefore,
$ \to 15x - 18x - 32x = - 52 - 17 - 22 + 21$
Now, carry out simple addition and subtraction and solve the equation. Therefore,
$ \to - 35x = - 70$
Now, divide both LHS and RHS with -35, we get
$
   \to \dfrac{{ - 35x}}{{ - 35}} = \dfrac{{ - 70}}{{ - 35}} \\
   \to x = 2 \\
 $
Hence, we have solved the equation $3\left( {5x - 7} \right) - 2\left( {9x - 11} \right) = 4\left( {8x - 13} \right) - 17$ and got the value of x equal to 2.

Note: Here, we can also cross check our answer by putting the value of x which is 2 in the given equation.
$
   \to 3\left( {5x - 7} \right) - 2\left( {9x - 11} \right) = 4\left( {8x - 13} \right) - 17 \\
   \to 3\left( {5 \times 2 - 7} \right) - 2\left( {9 \times 2 - 11} \right) = 4\left( {8 \times 2 - 13} \right) - 17 \\
   \to 3\left( 3 \right) - 2\left( 7 \right) = 4\left( 3 \right) - 17 \\
   \to 9 - 14 = 12 - 17 \\
   \to - 5 = - 5 \\
 $
Hence, LHS=RHS and our answer is correct.