Question

How do you solve \[3\left( {2x - 1} \right) - 2\left( {3x + 4} \right) = 11x?\]

Answer 1

Hint:This question describes the operation of addition/ subtraction/ multiplication/ division. To solve this type of question we need to move all the \[x\] terms into one side and all the constant terms into another side to make the easy calculation. In this type of question first, we need to solve the operations inside the parenthesis. We would try to eliminate the parenthesis and make it a simple equation.

Complete step by step solution:
The given equation is shown below,
\[3\left( {2x - 1} \right) - 2\left( {3x + 4} \right) = 11x \to \left( 1 \right)\]
At first, we would try to simplify the term\[3\left( {2x - 1} \right)\], it can be written as follows,
\[3\left( {2x - 1} \right) = 6x - 3 \to \left( 2 \right)\]
Next, we would try to simplify the term\[ - 2\left( {3x + 4} \right)\], it can be written as follows,
\[ - 2\left( {3x + 4} \right) = - 6x - 8 \to \left( 3 \right)\]
Let’s substitute the equations \[\left( 2 \right)\]and\[\left( 3 \right)\]in the equation\[\left( 1 \right)\], we get
\[
\left( 1 \right) \to 3\left( {2x - 1} \right) - 2\left( {3x + 4} \right) = 11x \\
6x - 3 - 6x - 8 = 11x \\
\]
To make an easy calculation, we would separate the \[x\] terms into one side. So, we get
\[6x - 3 - 6x - 8 - 11x = 0\]
Let’s separate the constant terms into another side, we get
\[6x - 6x - 11x = 8 + 3\]
In the above equation\[ + 6x\]and\[ - 6x\] can be canceled by each other. So we get
\[ - 11x = 11\]
So, we need to find the value of\[x\], for that let’s move \[ - 11\]to the right side of the equation.
So, we get
\[
x = \dfrac{{11}}{{ - 11}} \\
x = - 1 \\
\]
So, the final answer is,
\[x = - 1\]

Note: This type of question involves the operation of addition/ subtraction/ multiplication/ division. We would find the value of \[x\], for that, we should arrange the \[x\] terms into one side and constant terms into another side. If the negative sign is present in the denominator we can move it to the numerator.
Also, note the following things when multiplying different sign terms,
1) When a negative number is multiplied with a negative number, the answer becomes
positive.
2) When a positive number is multiplied with a negative number, the answer becomes
negative.
3) When a positive number is multiplied with the positive number the answer becomes
positive.