How do you solve the inequality $$3(k-5) + 9k ≥ -3$$ ?

First, distribute: $$3k - 15 + 9k ≥ -3$$ . Combine like terms: $$12k - 15 ≥ -3$$ . Add 15 to both sides: $$12k ≥ 12$$ . Finally, divide by 12: $$k ≥ 1$$ .

Solve the inequality $$-p - 4p > -10$$ .

Combine like terms: $$-5p > -10$$ . Divide by -5 (flip the sign): $$p

What is the solution to the inequality $$4(y-4)+8≤20$$ ?

Distribute: $$4y - 16 + 8 ≤ 20$$ . Combine like terms: $$4y - 8 ≤ 20$$ . Add 8 to both sides: $$4y ≤ 28$$ . Divide by 4: $$y ≤ 7$$ .

How do you solve the inequality $$-3(x+4)+3 ≥ 9$$ ?

Distribute: $$-3x - 12 + 3 ≥ 9$$ . Combine like terms: $$-3x - 9 ≥ 9$$ . Add 9 to both sides: $$-3x ≥ 18$$ . Divide by -3 (flip the sign): $$x ≤ -6$$ .

What happens to the inequality sign when you multiply both sides by a negative number?

The inequality sign flips direction when you multiply or divide both sides by a negative number.

Solve the inequality $$-3x ≥ 12$$ . Do I need to flip my sign?

Yes, divide by -3 (flip the sign): $$x ≤ -4$$ .

What is the solution to the inequality $$2x + 3

Subtract 3 from both sides: $$2x

What does it mean if an inequality has no solution?

An inequality has no solution if the variable cannot satisfy the inequality, such as $$x > x$$ .

How do you check your solution for an inequality?

Substitute the solution back into the original inequality to see if it holds true.

What is the solution to the inequality $$x + 5 ≤ 2x - 3$$ ?

Subtract x from both sides: $$5 ≤ x - 3$$ . Add 3 to both sides: $$8 ≤ x$$ or $$x ≥ 8$$ .

What is the importance of understanding multi-step inequalities?

Understanding multi-step inequalities is crucial for solving real-world problems that involve ranges of values, such as budgeting or measuring.

What is a compound inequality?

A compound inequality combines two inequalities, often connected by 'and' or 'or', representing a range of solutions.

Multi Step Inequalities Flashcards

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1.

FLASHCARD QUESTION

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.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

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