PDM Standard 3.B

Front

What is the definition of an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve the inequality |x + a| < b?

Back

To solve |x + a| < b, you split it into two inequalities: -b < x + a < b, and then solve for x.

Front

What is the solution set for the inequality |2x + 4| < 10?

Back

The solution set is -7 < x < 3.

Front

What is the definition of a logarithmic inequality?

Back

A logarithmic inequality is an inequality that involves a logarithm, which is the inverse operation of exponentiation.

Front

How do you solve the inequality log_b(x) < c?

Back

To solve log_b(x) < c, convert it to exponential form: x < b^c, ensuring x is within the domain of the logarithm.

Front

What is the solution set for the inequality log_6(x + 4) + log_6(3 - x) < 1?

Back

The solution set is -4 < x < -3 or 2 < x < 3.

Front

What is the definition of a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, typically in the form ax^2 + bx + c > 0 or similar.

Front

How do you solve the inequality x^2 - 4x - 5 > 0?

Back

First, factor the quadratic to (x - 5)(x + 1) > 0, then find the critical points and test intervals to determine the solution set.

Front

What is the solution set for the inequality x^2 - 4x - 5 > 0?

Back

The solution set is x < -1 or x > 5.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary points, while non-strict inequalities (≤, ≥) do include the boundary points.