Question

Solve for x: $7x - 5\left\{ {x - \left[ {7 - 6\left( {x - 3} \right)} \right]} \right\} = 3x + 1$ ?

Answer 1

Hint: The value of x in $7x - 5\left\{ {x - \left[ {7 - 6\left( {x - 3} \right)} \right]} \right\} = 3x + 1$can be found by using the method of transposition. Method of transposition involves doing the exact same mathematical thing on both sides of an equation with the aim of simplification in mind. This method can be used to solve various algebraic equations like the one given in question with ease.

Complete step-by-step solution:
We would use the method of transposition to find the value of x in $7x - 5\left\{ {x - \left[ {7 - 6\left( {x - 3} \right)} \right]} \right\} = 3x + 1$. Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding the value of the required parameter. We first open all the brackets and then simplify the expression obtained.
So, we have, $7x - 5\left\{ {x - \left[ {7 - 6\left( {x - 3} \right)} \right]} \right\} = 3x + 1$
Simplifying the expression further, we get,
$ \Rightarrow 7x - 5\left\{ {x - \left[ {25 - 6x} \right]} \right\} = 3x + 1$
$ \Rightarrow 7x - 5\left\{ {x - 7 + 6x - 18} \right\} = 3x + 1$
Simplifying the equation,
$ \Rightarrow 7x - 5\left\{ {7x - 25} \right\} = 3x + 1$
Opening the bracket, we get,
$ \Rightarrow 7x - 35x + 125 = 3x + 1$
Now, In order to find the value of x, we need to isolate x from the rest of the parameters.
So, we shift all terms consisting of x to the right side of the equation and rest all the terms to the left side of the equation. So, we get,
$ \Rightarrow 125 - 1 = 35x + 3x - 7x$
Simplifying the expression further, we get,
$ \Rightarrow 124 = 31x$
Dividing both sides of the equation by $31$, we get,
$ \Rightarrow x = 4$

Hence, the value of x in $7x - 5\left\{ {x - \left[ {7 - 6\left( {x - 3} \right)} \right]} \right\} = 3x + 1$ is $4$.

Note: There is no fixed way of solving a given algebraic equation. Algebraic equations can be solved in various ways. Linear equations in one variable can be solved by the transposition method with ease. If we add, subtract, multiply or divide by the same number on both sides of a given algebraic equation, then both sides will remain equal.