Question

How does a linear inequality different from a linear equation?

Answer 1

Hint: An inequality is a mathematical statement that shows that an expression is lesser than or more than the other. The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

Complete step by step solution:
The only difference between the two equations is that a linear equation gives a line graph whereas a linear inequality shows the area of the coordinate plane that satisfies the inequality. A linear inequality graph usually uses a borderline to divide the coordinate plane into two regions. The graph of linear inequalities includes a dashed line if they are greater than or less than but not equal to.
A linear equation will have one solution where as a linear inequality can have numerous.
For example: \[3x + 4 = 7\]
\[ \Rightarrow x = 1\]
Hence, we get only one solution
But, \[3x + 4 > 7\]
\[ \Rightarrow x > 1\]
Hence, every number larger than one is a correct solution.

Additional information:
Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, \[ < , > \] , \[ \leqslant , \geqslant \].These values could be numerical or algebraic or a combination of both. The linear inequality graph divides the coordinate plane into two parts by a borderline. This line is the line that belongs to the function.

Note: We must note that, the linear equation has only one variable usually and if any equation has two variables in it, then the equation is defined as a Linear equation in two variables. Linear equations, on the other hand, include a solid line in every situation. Moreover, linear inequalities include shaded regions whereas linear equations do not include shaded regions.