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can an absolute value inequality be negative

by Rosina Konopelski Published 3 years ago Updated 2 years ago

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. You can write an absolute value inequality as a compound inequality
compound inequality
A compound inequality contains at least two inequalities that are separated by either "and" or "or". The graph of a compound inequality with an "and" represents the intersection of the graph of the inequalities. A number is a solution to the compound inequality if the number is a solution to both inequalities.
https://www.mathplanet.com › solving-compound-inequalities

Solving compound inequalities - Algebra 1 - Math Planet

. This holds true for all absolute value inequalities.

Full Answer

How do you solve an inequality with absolute value?

  • Read the problem and highlight important information.
  • Identify the variables.
  • Find one piece of information in the problem that you can use to write an inequality.
  • Find a different piece of information that you can use to write a second inequality.

How to solve inequalities with absolute value?

The other case for absolute value inequalities is the "greater than" case. Solve | x | > 2, and graph. First, I'll start with a number line. The solution to the given inequality will be the set of all points that are more than two units away from zero. For instance, –3will work, as will +3; –4will work, as will +4.

How do you write an absolute value inequality?

What are some examples of inequalities?

  • Wage Inequality. …
  • Homelessness. …
  • Occupational Sex Segregation. …
  • Racial Gaps in Education. …
  • Racial Discrimination. …
  • Child Poverty. …
  • Residential Segregation. …
  • Health Insurance.

How to work with absolute value inequalities, step by step?

  • 3x+2| < 0 | 3 x + 2 | < 0
  • |x −9| ≤ 0 | x − 9 | ≤ 0
  • |2x−4| ≥ 0 | 2 x − 4 | ≥ 0
  • |3x−9| > 0 | 3 x − 9 | > 0

Can absolute value be a negative?

What Does Absolute Value Mean? Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Can an inequality be negative?

If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true. But if you multiply or divide both sides of an inequality by a negative number, the inequality is no longer true. In fact, the inequality becomes reversed.

Can absolute value be positive or negative?

positiveNo. Absolute value is always positive. Since it's the distance a number is from 0, it would always be positive.

Can an absolute value inequality be greater than or equal to a negative number?

The absolute value of something will never be less than or equal to a negative number. f. If the absolute value is greater than or greater than or equal to a negative number, the solution is all real numbers. The absolute value of something will always be greater than a negative number.

How do you solve inequalities with negative numbers?

Multiplying or dividing both sides by a negative number reverses the inequality. This means < changes to >, and vice versa. For example, given that 5 < 8 we can multiply both sides by 6 to obtain 30 < 48 which is still true. −30 > −48, which is a true statement.

What happens when you divide an inequality by a negative number?

There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

What is the absolute value of |- 10?

Number 10 has no sign i.e. it is positive and hence, we can say that |10|=10 . Graphically, absolute value of a number can be described as distance of its location on real number line from origin i.e. point described as 0 , irrespective of its direction, whether towards positive or negative side of origin.

What is the absolute value of -| 14?

Algebra Examples The absolute value is the distance between a number and zero. The distance between −14 and 0 is 14 .

What is the absolute value of |- 26?

The absolute value is the distance between a number and zero. The distance between −26 and 0 is 26 .

How do you know if it is absolute inequality?

Use the sign of each side of your inequality to decide which of these cases holds. If the number on the other side of the inequality sign is positive, proceed to step 3....Step 1: Isolate the absolute value|x + 4| - 6 < 9 |x + 4| < 15Step 4: Solve the compound inequality-19 < x < 112 more rows

What if there is a negative outside the absolute value?

If there is a negative sign outside the absolute value sign, then the value of the absolute is a negative number.

When can an equation containing an absolute value expression have negative values?

Since the absolute value of any number other than zero is positive, it is not permissible to set an absolute value expression equal to a negative number. So, if your absolute value expression is set equal to a negative number, then you will have no solution.

What are inequalities with absolute value

Before we analize inequalities with absolute value, let’s start by looking at a brief summary of the absolute value of a number.

How to solve inequalities with absolute value?

The steps to solve inequalities with absolute value are similar to the steps to solve equations, with the difference that we have to take into account a little extra information to solve the inequalities.

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