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Name Date Class LESSON37Practice B Solving AbsoluteValue InequalitiesSolve each inequality and graph the solutions. 1. x 2 32. X + 1 +5 7 3. 3x 6 94. X + 3 1.5 2.5 5. X + 17 20 6. X 6 7 3 7. 1 x +5
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How to fill out solving absolute-value inequalities

01
To fill out solving absolute-value inequalities, follow these steps:
02
Set up the inequality: Write out the absolute value inequality and ensure it is set to either greater than or less than.
03
Isolate the absolute value: Move any constant terms to the opposite side of the inequality.
04
Split the inequality: Consider two cases - one where the expression inside the absolute value is positive and one where it is negative.
05
Solve each case: Solve the two resulting inequalities separately for the variable.
06
Combine the solutions: Write the final solution as a compound inequality with 'or' between the two cases.
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Check your answer: Substitute the variable values into the original inequality to verify if the solution is valid.

Who needs solving absolute-value inequalities?

01
Solving absolute-value inequalities is often needed by students studying algebra and calculus.
02
It is particularly important for those who are working with equations involving absolute values.
03
Scientists, engineers, and other professionals also use absolute-value inequalities in various applications of mathematics.
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Absolute-value inequalities involve finding the range of values for a variable that satisfies the given absolute-value equation or inequality.
Students studying algebra or calculus may be required to solve absolute-value inequalities as part of their coursework.
To solve absolute-value inequalities, you first isolate the absolute value expression, then create two separate equations based on the positive and negative cases.
Solving absolute-value inequalities helps us determine the possible values that satisfy certain conditions and constraints.
The solutions or intervals where the variable satisfies the given absolute-value inequality.
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