How do you solve absolute value equations and inequalities?

How do you solve absolute value equations and inequalities?

Key Takeaways

1. To solve an absolute value equation, such as |X|=p, replace it with the two equations X=−p and X=p.
2. To solve an absolute value inequality involving “less than,” such as |X|≤p, replace it with the compound inequality −p≤X≤p and then solve as usual.

When would an absolute value inequality be all real numbers?

What do you get? Remember, the absolute value expression will yield a zero or positive answer which is always greater than a negative number. Therefore, the answer is all real numbers.

How do you solve absolute value equations with notes?

To Solve Absolute Value Equations:

1. Isolate the absolute value expression to one side of the equal sign.
2. Set the inside of the absolute value equal to + and to – the value on the other side of the equal sign (remove the absolute value bars in this step).
3. If needed, solve for the variable in these 2 new equations.

What does absolute value inequality mean in math?

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. These are less than (<), greater than (>), less than or equal (≤), and greater than or equal (≥).

How do you find the absolute value of an equation?

Absolute Value Equations and Inequalities. Absolute Value Definition – The absolute value of x, is defined as… = , ≥0 −, <0 where x is called the “argument”. Steps for Solving Linear Absolute Value Equations : i.e. += 1. Isolate the absolute value.

How to solve linear absolute value inequality step by step?

Steps for Solving Linear Absolute Value Inequalities : .# + ≤ 1. Isolate the absolute value. 2. Identify what the absolute value inequality is set “equal” to… a. If the absolute value is less than zero , there is no solution. b. If the absolute value is less than or equal to zero , there is one solution .

Can the absolute value of something be greater than the negative?

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.