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Solving Equations with absolute value and greater than inequalities Section 1-7 Algebra II R. Conyer EXAMPLE ONE |X| > 10 If the absolute value equation contains greater than inequality then you will set up two equations. X > 10 and X < -10 SOLUTION Step One: Set up the first equation using the original information. Set up the second equation by changing the greater than to less than and change positive ten to negative ten. EXAMPLE TWO |X - 4| > 12 Step One: X – 4 > 12 If the absolute value equation contains the greater than inequality then you will set up the following two equations. and X – 4 < -12 Step one: Set up the first equation using the original information. Set up the second equation by changing the greater than to less than and change positive twelve to negative twelve. Step Two: Solve both equations by adding four to each side of the equations. X – 4 > 12 +4 +4 0 16 Solution: X > 16 X – 4 < -12 +4 +4 0 -8 and X < -8 EXAMPLE THREE |3X + 7| > 16 Step One: 3X + 7 > 16 and If the absolute value equation contains the greater than inequality then you will set up two equations. 3X + 7 < -16 Step Two: Solve both equations by first subtracting seven from both sides of the equations. 3X + 7 > 16 -7 -7 0 9 3X > 9 and 3X + 7 < -16 - 7 -7 0 -23 and 3X < -23 Step Three: Solve the equations by dividing by both sides by three. 3X > 9 3 3 3X < -23 3 3 SOLUTION: X > 3 and X < -7.67