Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the interval notation \( (-9, \infty) \) represent?

Back

It represents all real numbers greater than -9, but not including -9.

Front

How do you solve the inequality \( 8x \geq -32 \)?

Back

Divide both sides by 8 to get \( x \geq -4 \).

Front

What is the graph of the inequality \( y \geq -5x - 3 \)?

Back

It includes all points above and on the line defined by the equation \( y = -5x - 3 \).

Front

Convert the inequality \( x \geq 100 \) into interval notation.

Back

The interval notation is \( [100, \infty) \).

Front

What does the symbol \( \geq \) mean in inequalities?

Back

It means 'greater than or equal to'.

Front

What is the solution set for the inequality \( x < 5 \)?

Back

The solution set in interval notation is \( (-\infty, 5) \).

Front

How do you represent the inequality \( y < 2x + 1 \) graphically?

Back

It is represented by a dashed line for \( y = 2x + 1 \) and includes all points below the line.

Front

What is the difference between \( \leq \) and \( < \)?

Back

\( \leq \) includes the boundary point, while \( < \) does not.

Front

How do you express the solution to \( 3x - 7 > 2 \)?

Back

Add 7 to both sides and then divide by 3 to get \( x > 3 \).