{"id":8650,"date":"2022-11-22T10:00:08","date_gmt":"2022-11-22T04:30:08","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=8650"},"modified":"2022-11-23T10:37:16","modified_gmt":"2022-11-23T05:07:16","slug":"absolute-value-inequalities","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/absolute-value-inequalities\/","title":{"rendered":"Absolute Value Inequalities"},"content":{"rendered":"
Solving an absolute value inequality problem is similar to solving an absolute value equation.<\/p>\n
Start by isolating the absolute value on one side of the inequality symbol, then follow the rules below:<\/p>\n
If the symbol is > (or >=) : (or)
\nIf a > 0, then the solutions to |x| > a
\nare x > a or x < – a.<\/p>\n
If a < 0, all real numbers will satisfy . |x| > a<\/p>\n
Think about it: absolute value is always positive (or zero), so, of course, it is greater than any
\nnegative number.<\/p>\n
If the symbol is < (or <=) : (and)
\nIf a > 0, then the solutions to |x| < a
\nare x < a and x > – a.
\nAlso written: – a < x < a.<\/p>\n
If a < 0, there is no solution to .|x| < a<\/p>\n
Think about it: absolute value is always positive (or zero), so, of course, it cannot be less than a negative number. To set up the two cases:<\/p>\n x < a x > -a <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n Read More:<\/strong><\/p>\n
\nRemember<\/strong>:
\nWhen working with any absolute value inequality,
\nyou must create two cases.
\nIf <, the connecting word is “and”.
\nIf >, the connecting word is “or”.<\/p>\n
\nCase 1<\/strong>: Write the problem without the absolute value sign, and solve the inequality.<\/p>\n
\nCase 2<\/strong>: Write the problem without the absolute value sign, reverse the inequality, negate the value NOT under the absolute value, and solve the inequality.<\/p>\n\n