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Solving graphical inequalities

When you solve simultaneous equations you are looking for an exact value of x and y that satisfies both of the equations. Inequalities are different!

An equation with an inequality represents, not a line, but an area. y< 3x + 5 means the area below the line y = 3x + 5 (not including the line itself!).

So when you have two inequalities, y< 3x + 5 and y>= 2x - 7 you are looking for the area that is both below 3x + 5 and greater than 2x - 7 (because it includes the equal condition, this one includes the line 2x - 7!).

Because we are looking at areas, that means that a solution is not necessarily on either of the lines, it could be anywhere inside the area.

That makes graphical calculators like Desmos very attractive for solving problems with inequalities. Desmos shades the areas, making it easy to see whether a point lies inside or outside the area. Usually much faster!

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