Solving Absolute Value Inequalities Part 1 Honors Math – Grade 8

Absolute Value Inequalities with < When solving an inequality of the form |x|<n, consider the following cases: 1. The expression inside the absolute value symbols is positive. 2. The expression inside the absolute value symbols is negative.

This means the distance from zero is less than 5 units. 5 units This shows an intersection. Write an inequality for each situation. x > -5x < 5 KEY CONCEPTAbsolute Value Inequalities with < ax + b > -candax + b < cmeans|ax + b|<c ax + b > -candax + b < cmeans|ax + b|<c

Solve the open sentence. Then graph the solution set. Write the inequality as a compound inequality using “and.” g + 5 < 4g + 5 > -4 Solve each inequality g < -1 g > -9 Therefore, g -9. Graph the solution set. The solution set represents an intersection. The solution set is: -9 < g < -1

Solve the open sentence. Then graph the solution set. Write the inequality as a compound inequality using “and.” n – 8 < 2n - 8 > -2 Solve each inequality n < 10 n > 6 Therefore, n 6 Graph the solution set. The solution set represents an intersection. The solution set is: 6 < n < 10

Solve the open sentence. Then graph the solution set. Write the inequality as a compound inequality using “and.” 2c + 5 < 32c + 5 > -3 Solve each inequality c < -2 c < -1 2c > -8 c > -4 Therefore, c -4. Graph the solution set. The solution set represents an intersection. The solution set is: -4 < g < -1

Solve Recall that the absolute value of a number is the distance from zero. This means that the absolute value of a number is always positive! Since l x + 2 l cannot be negative, l x + 2 l cannot be less than -7. So the solution is This is the symbol for the empty set. It means there is NO SOLUTION!