Question

How do you solve $4x + 2 = 3x - 7?$

Answer 1

As we know that a linear equation is an algebraic equation of the form $y = mx + b$, involving only a constant and a first order (linear) term, where $m$is the slope and $b$ is the $y$ -intercept.
These have the order equal to unity or one. The linear equation in one variable is written in standard form as $ax + b = 0$ i.e. only one variable. It is classified into different types based on the number of variables like linear equations in one variable or linear equations in two variables.

Complete step by step solution:
The equation of a straight line can be written in several forms. $y = mx + b$ is one of the forms of linear equations in one variable. To solve we need to isolate the $x$ term.
The equation is $4x + 2 = 3x - 7$. We need to first arrange all the similar terms together i.e. the $x$ term together and the numbers together. So we will get $4x - 3x = 7 - 2$, it gives $x = 5$.
Hence the required value of $x$ is $5.$

Note: We can always verify our solution by substituting the value into the left side of the equation and if it equals to the right side then it is the correct solution. This is a question of linear equation in one variable as it can be solved using the basic knowledge of arithmetic operators but while calculating we should be careful as in such types of question calculation mistakes are possible also with the positive and negative signs of the numbers and variables. As we know that if we make the graph of a linear equation it will have a straight line, this will happen when the highest power of the given variable is $1$ .