Solve for x x by simplifying both sides of the inequality, then isolating the variable. Inequality Form: − 5 4 < x < 5 2 - 5 4 < x < 5 2 Interval Notation: ( − 5 4 , 5 2 )
Move all terms not containing | 5 − 8 x | | 5 - 8 x | to the right side of the inequality. Tap for fewer steps... Add 7 7 to both sides of the inequality. | 5 − 8 x | < 8 + 7 | 5 - 8 x | < 8 + 7 Add 8 8 and 7 7 . | 5 − 8 x | < 15 | 5 - 8 x | < 15 Remove the absolute value term. This creates a ± ± on the right side of the inequality because | x | = ± x | x | = ± x . 5 − 8 x < ± 15 5 - 8 x < ± 15 Set up the positive portion of the ± ± solution. 5 − 8 x < 15 5 - 8 x < 15 Solve the first inequality for x x . Tap for more steps... x > − 5 4 x > - 5 4 Set up the negative portion of the ± ± solution. When solving the negative portion of an inequality, flip the direction of the inequality sign. 5 − 8 x > − 15 5 - 8 x > - 15 Solve the second inequality for x x . Tap for more steps... x < 5 2 x < 5 2 Set up the intersection. x > − 5 4 x > - 5 4 and x < 5 2 x < 5 2 Find the intersection between the sets. − 5 4 < x < 5 2 - 5 4 < x < 5 2 The result can be shown in multiple forms. Inequality Form: − 5 4 < x < 5 2 - 5 4 < x < 5 2 Interval Notation: ( − 5 4 , 5 2 ) ( - 5 4 , 5 2 )
