# Solving Inequality Problems

An absolute value equation is an equation that contains an absolute value expression.The equation $$\left | x \right |=a$$ Has two solutions x = a and x = -a because both numbers are at the distance a from 0.To solve an absolute value equation as $$\left | x 7 \right |=14$$ You begin by making it into two separate equations and then solving them separately.$$x 7 =14$$ $$x 7\, \, =14\, $$ $$x=7$$ or $$x 7 =-14$$ $$x 7\, \, =-14\, $$ $$x=-21$$ An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

Even though the right side was a -10, the number we were dividing both sides by, was a positive 5.Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument.To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem.But, when a variable is less than or greater than a number, there are an infinite number of values that would be a part of the answer.is less than 4' means that if we put any number less than 4 back in the original problem, it would be a solution (the left side would be less than the right side).A manufacturer has 600 litres of a 12 percent solution of acid.How many litres of a 30 percent acid solution must be added to it so that the acid content in the resulting mixture will be more than 15 percent but less than 18 percent?Basically, we still want to get the variable on one side and everything else on the other side by using inverse operations.The difference is, when a variable is set equal to one number, that number is the only solution.Graph: Since we needed to indicate all values greater than or equal to -5, the part of the number line that was to the right of -5 was darkened.Since we are including where it is equal to, a closed hole was used.

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It took me a long time to realize that all those displays of tough, patriotic love were meant to inoculate me against the rigors that face all other Filipinos…