What is linear in equalities in two variable

A linear inequality in two variables takes the form:

y>m x+b or y<m x+b. ( where x and y are two variables)

Linear inequalities are closely related to graphs of straight lines; recall that a straight line has the equation y=m x+b.

The solution to a linear inequality includes all the points in one half of the plane. We can tell which half by looking at the inequality sign:

> The solution set is the half plane above the line.

≥ The solution set is the half plane above the line and also all the points on the line.

< The solution set is the half plane below the line.

≤ The solution set is the half plane below the line and also all the points on the line.

"We use dotted line for a strict inequality and solid line for an inequality sign which also include equality" .

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions