How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation and put an inequality sign in its place, is there ever a time when the same value will be a solution to both the equation and inequality?

Question

anonymous · Answer

you plug the value in and see if the inequality is true or not.  It is different than an equation because in an equation the two expressions must be exactly equal, but in an inequality (for example 2+x<5) x can be anything less than 3. If we had 2+x=5 then x could only be 3.  A value can be a solution to both an inequality and equation if there is a "less than or equal to" or "greater than or equal to" sign involved:

$$2+x \le5, 2+x=5$$

x=3 is a solution to both of these.
if the sign on the inequality was strictly less than or greater than there would be no solutions to both the equation and inequality