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 3x7<2x+5

Determining if the Point is a Solution

Consider the inequality 2x3>5. Determine if the point x=5 is a solution to this inequality.

Quadratic Inequalities

Solve the quadratic inequality 2x25x+3>0.

Rational Inequalities

Solve the rational inequality x29x24x+40.

Converting from Interval to Inequality

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

Converting to Interval Notation

Solve the inequality 3x7>2x+5 and write the solution in interval notation.

Rewriting as a Single Interval

Solve the inequality 2x3>5 and 3x+2<14 and express the solution as a single interval.