Inequalities

Inequalities are used to articulate the connection between two expressions or values that aren't equivalent. The symbols utilized in inequalities include less than (<), greater than (>), less than or equal to (≤), and greater than or equal to (≥). The process of solving inequalities is centered around determining the spectrum of values that make the inequality true.

Solving for a Variable

Solve the inequality \(3x - 7 < 2x + 5\)
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Determining if the Point is a Solution

Consider the inequality \(2x - 3 > 5\). Determine if the point \(x = 5\) is a solution to this inequality.
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Quadratic Inequalities

Solve the quadratic inequality \(2x^2 - 5x + 3 > 0\).
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Rational Inequalities

Solve the rational inequality \(\frac{x^2 - 9}{x^2 - 4x + 4} \leq 0\).
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Converting from Interval to Inequality

Convert the interval (-3, 7] to inequality form.
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Converting to Interval Notation

Solve the inequality \(3x - 7 > 2x + 5\) and write the solution in interval notation.
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Rewriting as a Single Interval

Solve the inequality \(2x - 3 > 5\) and \(3x + 2 < 14\) and express the solution as a single interval.
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