Question

Solve the equation \[8\left( {2x - 5} \right) - 6\left( {3x - 7} \right) = 1\] and find the value of x?

Answer 1

Hint: We must solve this for ‘x' in the given problem. We can use the transposition method to solve this. The most common transposition method involves doing the same thing (mathematically) to both sides of the equation in order to group like terms together and isolate the variable (or the unknown quantity). That is, we group the ‘x' terms on one side of the equation and the constants on the other.

Complete step by step answer:
We have given equation is \[8\left( {2x - 5} \right) - 6\left( {3x - 7} \right) = 1\]
We will first eliminate the brackets and do multiplication
\[ \Rightarrow 16x - 40 - 18x + 42 = 1\]
 We will transpose -40 and +42 to the right-hand side of the equation.
\[ \Rightarrow 16x - 18x = 1 - 42 + 40\]\[\]
We will simplify both side
\[ \Rightarrow - 2x = - 1\]
We divide the both side by -2,
\[ \Rightarrow x = \dfrac{1}{2}\]
The value of x is \[\dfrac{1}{2}\] .

Note:
There are three methods to solve linear equations in one variable.
1. Trial and Error.
2. Inverse operations.
3. Transposition Method.