document.write( "Question 1191819: Write the inequality and solve the problem: The difference of a number and 8 is less than 12. \n" ); document.write( "
Algebra.Com's Answer #823665 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "x = unknown number
\n" ); document.write( "x-8 = difference of the number and 8
\n" ); document.write( "x-8 < 12 ... the result of translating the sentence into an inequality
\n" ); document.write( "i.e. the difference x-8 is smaller than 12\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To solve this inequality, we add 8 to both sides.
\n" ); document.write( "This undoes the \"minus 8\" on the left side so x can be isolated.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "x-8 < 12
\n" ); document.write( "x-8+8 < 12+8
\n" ); document.write( "x+0 < 20
\n" ); document.write( "x < 20\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The unknown number is smaller than 20\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For example, we could pick the value x = 15
\n" ); document.write( "x-8 < 12
\n" ); document.write( "15-8 < 12
\n" ); document.write( "7 < 12
\n" ); document.write( "we end up with a true statement, so the original statement is true when x = 15\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On the other hand, if x is something larger than 20 (or 20 itself), then we get a false result.
\n" ); document.write( "Let's try something like x = 30
\n" ); document.write( "x-8 < 12
\n" ); document.write( "30-8 < 12
\n" ); document.write( "22 < 12
\n" ); document.write( "which is false\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To graph x < 20 on the number line, you'll have an open circle at 20 and shading to the left.
\n" ); document.write( "The open circle will exclude the endpoint.
\n" ); document.write( " \n" ); document.write( "
\n" );