Use inequalities involving absolute values to solve the...

Use inequalities involving absolute values to solve the given problems.
The voltage $v$ in a certain circuit is given by $v=6.0-200 i$ where $i$ is the current (in $\mathrm{A}$ ). For what values of the current is the absolute value of the voltage less than $2.0 \mathrm{V} ?$

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Key Concepts

Compound Inequalities

Compound inequalities combine two simpler inequalities into one statement, such as -c < expression < c. This form allows us to isolate the variable by performing the same operations on all parts of the inequality, ensuring that all conditions imposed by the original absolute value inequality are met.

Absolute Value

The absolute value of a number represents its distance from zero on the number line, regardless of its direction. It is used in equations and inequalities to express constraints on how far a number can be from a certain value without considering its sign.

Absolute Value Inequalities

Linear Functions in Circuit Analysis

Linear functions, such as the equation given for voltage in a circuit, describe relationships where the change in one variable is proportional to the change in another. Understanding how to manipulate and interpret linear functions is essential in applying mathematical concepts, such as absolute value inequalities, to real-world problems in circuits and other fields.

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