{"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":"

Absolute Value Inequalities<\/strong><\/span><\/h2>\n

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.
\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

To set up the two cases:<\/p>\n

x < a
\nCase 1<\/strong>: Write the problem without the absolute value sign, and solve the inequality.<\/p>\n

x > -a
\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

\"Absolute-Value-Inequalities-1\"<\/p>\n

\"Absolute-Value-Inequalities-2\"<\/p>\n

\"Absolute-Value-Inequalities-3\"<\/p>\n

\"Absolute-Value-Inequalities-4\"<\/p>\n

\"Absolute-Value-Inequalities-5\"<\/p>\n

Read More:<\/strong><\/p>\n