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10 Questions & Answers Absolute value equations and inequalities Solving linear equations and inequalities * If you want to know how to solve these ten questions do it on a separate sheet of paper. Try solving them to the best of your abilities before clicking to see the answers. Solving absolute value equations and Inequalities • Goal 1: solving equations and inequalities • Absolute value of a number x, is written like this IxI, is the distance the number is from 0 on a number line. Always remember absolute value is always nonnegative. The distance between -4 and 0 is 4, so I-4I=4 The distance between 4 and 0 is 4, so I4I=4 • Lets start with some examples… Rewrite the absolute value equation as two linear equations and then solve each linear equation. • Ex 1) Solve I2x-5I=9 • I2x-5I=9 Write original equation • 2x-5=0 -9 or 2x-5=-9 • 2x=14 or 2x=-4 • X=7 or x=-2 expression can be 9 or add 5 to each side divide each side by 2 Lets try 2 one your own… •Rewrite the absolute value equation as two linear equations. • Ex 2) solve I5n4I=16 • Check your answer after you finished solving. • 5n-4=16 or 5n4=-16 • 5n=20 12 or • n= 4 12/5 or Ex 3) solve I 8x+1I=23 Check your answer after you finished solving. • 8x=1=23 or 8x=1=-23 • 8x=22 or 8x=-24 • X= 22/8 or x= -3 5n=- n= - Practice makes perfect… • Rewrite the absolute value equation as two linear equations. 1. Ix+5I=4 2. Ix-3I=2 3. I3x+4I=2 0 4. I4x• Decide whether the given number is a solution of the 7I=13 equation. 5. I3x+8I =20: -4 6. I2x-9I= 11: -1 7. I-x+9I = 4: -5 8. I3x+6I = 0: -2 Answers • • • • • • • • 1. x= -1,-9 2. x= 5,1 3. x=16/3,-8 4. x= 5, -3/2 5.no 6. yes 7.no 8. yes