Question

How do you solve the equation $28 = 14 + 7\left( {x - 6} \right)$?

Answer 1

This is a linear equation in only one variable. Take constants on one side and the term having variables on the other side. Then divide both sides of the equation with a suitable number to find the value of the variable.

Complete step by step answer: According to the question, a linear equation in one variable is given to us and we have to solve it.
The given equation is:
$\Rightarrow 28 = 14 + 7\left( {x - 6} \right)$
For solving this, first we’ll transfer 14 from right hand side to left hand side of the equation, we’ll get:
$\Rightarrow 28 - 14 = 7\left( {x - 6} \right)$
This equation can also be written as:
$\Rightarrow 7\left( {x - 6} \right) = 28 - 14 \\\ \Rightarrow 7\left( {x - 6} \right) = 14 \\\$
Dividing both sides of the equation by 7, well get:
$\Rightarrow \dfrac{{7\left( {x - 6} \right)}}{7} = \dfrac{{14}}{7} \\\ \Rightarrow \left( {x - 6} \right) = 2 \\\$
Again transferring 6 from left hand side to right hand side of the equation, we’ll get:
$\Rightarrow x = 2 + 6 \\\ \Rightarrow x = 8 \\\$
Thus the value of variable $x$ in the equation is 8.

Additional Information:
An equation in one variable with the highest power of variable in the equation as 1 is called a linear equation in one variable. If the highest power is 2 then it is called a quadratic equation and if the highest power is 3 then it is called a cubic equation. To generalize it, if the highest power is n then it is called the nth degree equation.
This condition is valid if all the powers of the variable throughout the equation are non negative integers.

Note:
If a linear equation is having only one variable, it can be solved directly to get the value of the variable. If it was a two variable equation, we couldn’t have solved it. To determine the values of two different variables, we need a system of two different equations in those variables and to determine three variables we need a system of three equations in those variables. Similarly if there are $n$ different variables then we require $n$ different equations to find their values.