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Absolute Value Equations
How do you graph this:(2x + 1) = 3Substitute the parenthesis with Absolute Value thingy
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**** ***** ******** * * ******** 2×=-4 ***** Or 2x+1=3 **** *** ** *** ***** ********** ****** *** *** These two **** intersect ** x=-2 *** * = * **** solution ** the ******** ********* *********** **** for the *****
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** **** *** ********* ** * 1| * * as the absolute value ******** Now ** *** *** ********** of ******** ***** *********** = a ** **** *** ******** of ' x * as follows * ** * ** * ve ******* =a ***** x|= a **** = * ** * ** *** ******* ** ⇒-x * * **** = -a(∵|x| *** ** = * *** ** *** above ********** ** **** * ********** as follows ** * ** ( **** ) ** * ** ***** ** + 1| * * *** ** * 1 = **** ** ** ** * * ** ************ 1 on **** ***** * ⇒ 2x * * *** ** ** * * ** * ******** **** ***** ** 2 **** * * * So ** **** * * 1 as ******** *** x if ( ** * * * ** * ** *** * **** * ** *** ***** ** * 1| * * *** (2x + *** ***** ** +1 ** * -3 -1 (Subtracting * ** **** ***** * *** ** = -4 *** 2x ** = **** ( ******** both sides ** 2 **** x * ** ** ** **** * * **** ******** for * ** * ** + 1 ) ** -ve ** we **** got * solutions *** * namely * * 1 and x * **** now plot these solutions *** * ** * ********* graph ** * ***** * **** ****** ***** the ******** **** ***** ***** *** ***** of the ********* of * ** * = * *** x * ** ** * *** * **** *** **** **** *** *** *********** ** -1 ** -3 -----01 * 3 4 5 ** *** * **** and ********* ** -2 ** -4 ** * * 3 * * on the * axis *** **** **** *** origin **** * * *********** ** **** *** ******** of * = * ** *** ***** ** **** * ******** **** ** * **** ** a distance ** * **** *** * **** All the ****** ** **** * axis will **** * ********** ** * Similarlyto **** *** ******** ** x = **** *** ***** we draw a ******** line ** * axis ** * distance of ****** *** y axis *** *** points ** **** y **** will **** x ********** ** -2 ** * * * *** * = ** *** the solutions *** x ** ***** ** *** ***** ********** * ***** y ****