You have learned how to solve a conjunction of two inequalities. You have also learned how to translate phrases into algebraic expressions and solve problems by writing and solving equations. Solve the following problems. Click “Submit” when finished.

You have learned how to find the solution to a problem by translating it into an equation and then solving the equation. Some problems are expressed best by inequalities, rather than equations. For example, the statement a number <EQUATION> is less than <EQUATION> can be represented by the inequality <EQUATION>.

Similarly, the statement “a number <EQUATION> is greater than or equal to <EQUATION>” can be represented by the inequality <EQUATION>. Now, let’s translate the statement “a number <EQUATION> is at least <EQUATION>.” If a number is at least <EQUATION>, then it can be <EQUATION> or greater. So this statement translates to the inequality <EQUATION>.

Translate the statement “a number <EQUATION> is at most 4” into an inequality and graph its solutions. Click “Submit” when finished.

Now, translate the statement “-1 is greater than or equal to some number <EQUATION>” into an inequality and graph its solution set. Click “Submit” when finished.

Match each inequality symbol with the words that describe it. Click “Submit” when finished.

Now let’s translate the statement “12 more than <EQUATION> times a number is greater than 14” using inequalities. “12 more than” means that 12 is added to some value. If we let <EQUATION> represent the number, then “3 times a number” is <EQUATION>. Now, we translate “is greater than” using the inequality symbol. Completing the statement, we have <EQUATION>.

Now, let’s translate the statement “5 less than twice a number is at most <EQUATION>.” “5 less than” means that 5 is subtracted from some value. If we let <EQUATION> represent the number, then “twice a number” is <EQUATION>. You know that “at most” translates to <EQUATION>. Completing the statement, we have <EQUATION>.

Now, translate the statement “3 less than a number is greater than the opposite of the number.” Click “Submit” when finished.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education