How do you know if an absolute value inequality is AND or OR?

If it is a conjunction that uses the word and, the solution must work in both inequalities and the solution is in the overlap region of the graph. If it is a disjunction that uses the word or, the solution must work in either one of the equations.

What is inequality involving absolute value?

An absolute value inequality is an expression with absolute functions as well as inequality signs. For example, the expression |x + 3| > 1 is an absolute value inequality containing a greater than symbol. There are four different inequality symbols to choose from.

What’s the difference between and and/or in inequalities?

The key difference is with “or”, x only needs to satisfy one of the inequalities. With “and”, x needs to satisfy both.

How do you know if an absolute value inequality has no solution?

Here are the steps to follow when solving absolute value inequalities:

Isolate the absolute value expression on the left side of the inequality.
If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.

How are absolute values solved?

To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations.

How many solutions are there if an absolute value inequality holds true to all values of real numbers?

The answer to this case is always no solution. The absolute value of any number is either zero (0) or positive. It makes sense that it must always be greater than any negative number. The answer to this case is always all real numbers.

What are two variable inequalities?

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.