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Absolute value inequalities worksheet

Absolute value inequalities worksheet 2025

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The document contains extra practice problems for Algebra 1, focusing on absolute value equations and inequalities. It includes two parts: the first part requires students to solve various absolute value equations, while the second part involves determining the nature of solutions for given absolute value inequalities without solving them. Students are instructed to show their work on a separate piece of paper.

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How to solve absolute value equations notes?

To Solve Absolute Value Equations: Isolate the absolute value expression to one side of the equal sign. 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). If needed, solve for the variable in these 2 new equations.

What is the rule for solving absolute value equations?

Absolute value equations can yield two solutions because the absolute value of any number and its opposite is equal to the same value. This follows the rule |x| = k is equivalent to x = k or x = -k if and only if k is greater than or equal to 0.

How to tell if an absolute value inequality is no solution?

If the absolute value is less than or less than or equal to a negative number, there is no solution. 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.

What are the notes on absolute value functions?

Important Notes on Absolute Value Function An absolute value function is a function in algebra where the variable is inside the absolute value bars. The graph of an absolute value function is always either V-shaped or inverted V-shaped depending upon the value of a.

How to solve absolute value equations step by step?

3:36 4:20 So if we add one x is equal to four and if we add one to the other one negative three plus one isMoreSo if we add one x is equal to four and if we add one to the other one negative three plus one is negative two. So this is the solution.

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How do you note absolute value?

The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines. |6| = 6 means the absolute value of 6 is 6.

How do you solve absolute value inequalities?

To solve inequalities with absolute values, use a number line to see how far the absolute value is from zero. Split into two cases: when it is positive or negative. Solve each case with algebra. The answer is both cases together, in intervals or words.

How do you graph an absolute value system of inequalities?

Graph the line for the corresponding equation, use a solid line if the the inequality includes equal to and a broken line if it does not, shade in the area above for greater than, shade in the area below for less than.

Absolute value inequalities worksheet 2025

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