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# What does a solution for one linear inequality look like? How is that different from a solution for one linear equation?

What does a solution for one linear inequality look like? How is that different from a solution for one linear equation?

A linear inequality in the plane is an expression of the form, for example, 4x-2y<3.
This may be rewritten in the form 2y>4x-3 or y>2x-3/2.  The y-values are all of those greater than those on the line y=2x-3/2.  The area defined by this is the part of the plane above, but not on the line y=2x-3/2.

For another example ax+by≤c, where a,b,c are real numbers.  Assume that b≠0 and have
by≤c-ax.  If b>0 then this becomes y≤-(a/b)x+c/b, and so refers to all of the points on or below the line y=-(a/b)x+c/b.
If b<0 then the inequality is reversed and is y≥-(a/b)x+c/b and refers to all the points on or above the line
y=-(a/b)x+c/b

Try the examples y>3 or x<2 yourself.

A linear equation specifies only the points on a line in the plane, and not an area in the plane.
Great question Elton!

First, lets talk about what linear means.  Linear means the rate of change of this line is not exponential and will never change, the slope will always remain the same at every point on this line.

A linear inequality will contain the greater than (>) or less than (<) symbols.  Where a linear equation will have an equal (=) sign instead.

Ex: x +3 > 5 => subtract 3 from both sides => x > 2.  All values greater than 2 will meet the criteria for this linear inequality.

The linear inequality solution will be a range of numbers as opposed to the linear equation will be one single number.

Ex: x + 3 = 5 => subtract 3 from both sides => x = 2.  Only the value of 2 meets the criteria and is the solution to this linear equation.