Multi-Step & Compound Inequalities

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality 6x + 10 > 5x - 12?

Back

Subtract 5x from both sides: x + 10 > -12. Then, subtract 10: x > -22.

Front

What does the solution x > -22 represent on a number line?

Back

It represents all numbers greater than -22, extending to the right on the number line.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often using 'and' or 'or' to connect them.

Front

How do you solve the compound inequality -3 ≤ 2x - 1 ≤ 5?

Back

Add 1 to all parts: -2 ≤ 2x ≤ 6. Then divide by 2: -1 ≤ x ≤ 3.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) or [a, b].

Front

Write the interval notation for the solution x ≥ 2 and x ≤ 4.

Back

[2, 4]

Front

What does the inequality x < 3 mean?

Back

It means that x can be any number less than 3.

Front

How do you express the solution to the inequality 2x + 4 < 10 in words?

Back

The solution is all values of x that are less than 3.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one condition must be true.