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vilhelm
- 37
- 0
Solve 2x - |x+1| < 4.
Inequality with absolute value refers to mathematical inequalities that involve absolute value symbols. These symbols indicate the distance of a number from zero on a number line, and when used in inequalities, they can represent a range of numbers that satisfy the inequality.
To solve an inequality with absolute value, first isolate the absolute value expression on one side of the inequality. Then, rewrite the absolute value as a compound inequality with two separate inequalities, one for the positive value and one for the negative value. Solve each inequality separately to find the solution set.
Understanding inequality with absolute value is important because it allows us to accurately represent and solve real-world problems involving ranges of values. It also helps us to understand the concept of distance on a number line and how it relates to inequalities.
Yes, an inequality with absolute value can be graphed on a number line. The solution set will be represented by a shaded region on the number line, with the absolute value symbol indicating the distance from zero.
Yes, common mistakes when solving inequalities with absolute value include not correctly isolating the absolute value expression, forgetting to write the compound inequality, and not considering both the positive and negative solutions. It's important to carefully follow the steps and check your work to avoid these mistakes.