Absolute Value Expressions and Equations

Expressions involving absolute values are concerned with the measurement of a number's distance from zero on the number line, independent of its direction. On the other hand, absolute value equations are about determining the range of values that satisfy the given equation. The solution process entails separating the absolute value expression and taking into account both the positive and negative potential outcomes.

Simplifying Absolute Value Expressions

Simplify the expression \(|2x - 3| - |x - 1|\) when \(x < 1\)
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Solving with Absolute Values

QUESTION 3 - 1 POINT Find the solutions to the following absolute value equation. \[ 7|x+5|+4=8 \] Separate multiple answers with a comma. Provide your answer below: \[ x= \]
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Finding the Vertex for the Absolute Value

EXAM REVISION 2 1. The diagram shows a sketch of part of the graph $y=f(x)$ where $f(x)=3|x-4|-5$ Figure 2 a State the range of $f$. $b$ Given that $\mathrm{f}(x)=-\frac{1}{3} x+k$, where $k$ is a constant has two distinct roots, state possible values of $k$.
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Rewriting the Absolute Value as Piecewise

Solve the absolute value equation \( |2x - 5| = 3 \).
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Popular Problems

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