What is different between solving inequalities and absolute value inequalities?

Answer:The absolute number of a number a is written as|a|And represents the distance between a and 0 on a number line.An absolute value equation is an equation that contains an absolute value expression. The equation|x|=aHas two solutions x = a and x = -a because both numbers are at the distance a from 0.To solve an absolute value equation as|x+7|=14You begin by making it into two separate equations and then solving them separately.x+7=14x+7−7=14−7x=7orx+7=−14x+7−7=−14−7x=−21An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.The inequality|x|<2Represents the distance between x and 0 that is less than 2Whereas the inequality|x|>2Represents the distance between x and 0 that is greater than 2You can write an absolute value inequality as a compound inequality.−2<x<2This holds true for all absolute value inequalities.|ax+b|<c,wherec>0=−c<ax+b<c|ax+b|>c,wherec>0=ax+b<−corax+b>cYou can replace > above with ≥ and < with ≤.When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.Step-by-step explanation:Hope this helps :)