Question

Find the value of x in the equation $ - 4\left( {2 + x} \right) = 8$

Answer 1

Hint: Given an equation is a linear equation because the highest exponent of x is 1. To solve the given equation send all the constant terms to the RHS and variable terms to LHS. Then solve for x.

Complete step-by-step answer:
We are given an equation $ - 4\left( {2 + x} \right) = 8$ and we have to find the value of x.
In the given equation, the left hand side and right hand side, both sides have the highest power of x is 1. So, the given equation is a linear equation in one variable.
$ - 4\left( {2 + x} \right) = 8$
Multiplying -4 to the portion in the brackets on left hand side
$
 \left( { - 4 \times 2} \right) + \left( { - 4x} \right) = 8 \\
  \to - 8 - 4x = 8 \\
 $
Multiplying negative sign on LHS and RHS
$
  \to - \left( { - 8 - 4x} \right) = - 8 \\
  \to 8 + 4x = - 8 \\
 $
Sending 8 in the left hand side to the right hand side
$
 4x = - 8 - 8 \\
 \to 4x = - 16 \\
 $
Now dividing -16 with 4 to get the value of x
$
  x = \dfrac{{ - 16}}{4} \\
  \therefore x = - 4 \\
 $
Therefore, the value of x is -4.
Substitute the value of x in $ - 4\left( {2 + x} \right) = 8$ to verify.
$
 - 4\left( {2 + \left( { - 4} \right)} \right) = 8 \\
 \to - 4 \times - 2 = 8 \\
 \to 8 = 8 \\
 $
LHS=RHS, therefore the value we got is correct.


Note: A linear equation has only one solution or one root as the highest degree is 1, a quadratic equation will have two solutions or two roots as the highest degree is 2. Therefore, the no. of solutions for equations increases with increase in their degrees.
A linear equation is an equation of a straight line having maximum one variable. The power of the variable will be 1. To solve any equation in one variable, put all the variable terms on the left hand side and all the numerical values on the right hand side for an easy approach.