Question

How do you solve $4x - 2\left( { - 5x + 4} \right) = 62$?

Answer 1

Hint: The above question is a linear equation in one variable. We need to solve it to get the value of ‘x’. In order to solve it, we need to expand the equation, take all the terms with ‘x’ on one side of the equation, and the constant terms on the other. Then, we divide both sides of the equation with the coefficient of ‘x’, which gives us the desired value.

Complete step by step solution:
We need to solve the equation: $4x - 2\left( { - 5x + 4} \right) = 62$
This is a linear equation in one variable, as such, we will get a unique value of the variable ‘x’.
$4x - 2\left( { - 5x + 4} \right) = 62$
On expanding this equation, we get:
$ \Rightarrow 4x + 10x - 8 = 62$
Then, we add all the coefficients of ‘x’ and replace all the ‘x’ terms with a single term. Also, the coefficients are written on the other side.
$
   \Rightarrow \left( {4 + 10} \right)x = 62 + 8 \\
   \Rightarrow 14x = 70 \\
 $
Now, dividing both sides of the above equation by 14, we get:
$ \Rightarrow \dfrac{{14x}}{{14}} = \dfrac{{70}}{{14}}$
Solving further, we get:
$ \Rightarrow x = 5$
Thus, the solution for the equation $4x - 2\left( { - 5x + 4} \right) = 62$, is $x = 5$

Note: In this type of equation (linear equation in one variable), the expressions which are involved in the formation of the equation are made up of only one variable, i.e., the highest power of the variables used in the equation is 1. The solution to this linear equation can be any rational number. Such equations may also consist of expressions which are linear on both sides of the equal to sign.

Just like numbers can be transposed from one side of the equation to the other, as in the above problem, we can also transpose the variables. Utilization of linear equations can be seen in diverse scenarios such as problems on numbers, perimeter, ages, currency, etc.