9.3 Solve Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'.

Front

How do you solve the inequality d + 7 ≥ 30?

Back

Subtract 7 from both sides: d ≥ 30 - 7, so d ≥ 23.

Front

What is the solution set for the inequality 5z - 2 - 2z < 13?

Back

Combine like terms: 3z - 2 < 13, then add 2: 3z < 15, and divide by 3: z < 5.

Front

What does the inequality x > -3 represent?

Back

It represents all values of x that are greater than -3.

Front

How do you interpret the inequality h ≥ 48 in a real-world context?

Back

It means a person must be at least 48 inches tall to ride the bumper cars.

Front

What is the solution to the inequality 8(m + 2) < 4(5 + 2m)?

Back

This inequality simplifies to all real numbers, meaning any value of m satisfies it.

Front

What does the symbol '<' indicate in an inequality?

Back

The symbol '<' means 'less than'.

Front

What is the first step in solving the inequality 10 < 3x + 19?

Back

Subtract 19 from both sides: 10 - 19 < 3x, which simplifies to -9 < 3x.

Front

What does the solution z < 1 mean?

Back

It means z can take any value less than 1.