What is integer inequalities with absolute values?

If we see a problem with an absolute value that is less than 0, then the answer will always be no solution. If we see a problem with the absolute value being greater than a negative number, then the answer will be all x.

How do you solve negative absolute value inequalities?

To solve for negative version of the absolute value inequality, multiply the number on the other side of the inequality sign by -1, and reverse the inequality sign: | 5 + 5x | > 5 → 5 + 5x < − 5 => 5 + 5x < -5 Subtract 5 from both sides => 5 + 5x ( −5) < −5 (− 5) => 5x < −10 => 5x/5 < −10/5 => x < −2.

How to solve integer inequalities with absolute values?

Solving inequalities with absolute values uses the same techniques as solving for inequalities. We remember that if we divide or multiply by a negative number, then our inequality flips. To start solving an inequality with absolute value is to set up two inequalities to solve. The first inequality will be our problem without the absolute value.

When is an absolute value equation has no solution?

As we are solving absolute value equations it is important to be aware of special cases. An absolute value is defined as the distance from 0 on a number line, so it must be a positive number. When an absolute value expression is equal to a negative number, we say the equation has no solution, or DNE.

How to find the absolute number of a number?

The absolute number of a number a is written as. $$\\left | a \\right |$$. And represents the distance between a and 0 on a number line. An absolute value equation is an equation that contains an absolute value expression. The equation. $$\\left | x \\right |=a$$. Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

Which is an example of an absolute value?

For any positive value of a and x, a single variable, or any algebraic expression: Let’s look at a few more examples of inequalities containing absolute values. Since this is a “greater than” inequality, the solution can be rewritten according to the “greater than” rule.