Definition
Solution of an inequality
A solution of an inequality is a value that makes the inequality true.
What it means
Treat a possible value like a key and test it in the inequality. If the statement becomes true, the value fits and is a solution. Many inequalities have a whole set of solutions rather than one answer.
Remember it
A solution passes the true-or-false test.
Example
Test x = 7 in x > 5. Substitution gives 7 > 5, which is true, so 7 is a solution. Testing x = 5 gives 5 > 5, which is false, so 5 is not a solution.
Watch for
A boundary value is included only when the symbol allows equality, as in ≤ or ≥.
Common mix-up
An inequality often has many solutions; do not stop after finding one value that works.
Exact meaning
A solution of an inequality is any value, or ordered pair for a two-variable inequality, that makes the inequality a true statement when substituted.