How do you solve the inequality $$9 \\le 2m + 2 - 3$$ ?

To solve the inequality, first simplify: $$9 \\le 2m - 1$$ . Then add 1 to both sides: $$10 \\le 2m$$ . Finally, divide by 2: $$5 \\le m$$ or $$m \\ge 5$$ .

What does the graph of $$m \\ge 5$$ look like?

The graph of $$m \\ge 5$$ is a number line with a closed circle at 5 and shading to the right, indicating all values greater than or equal to 5.

What is the solution set for the inequality $$2(x + 6)

To solve, first distribute: $$2x + 12

How do you match a graph to the inequality $$-5(x + 3) + 2x > -6$$ ?

First, simplify the inequality: $$-5x - 15 + 2x > -6$$ . Combine like terms: $$-3x - 15 > -6$$ . Add 15 to both sides: $$-3x > 9$$ . Finally, divide by -3 (remember to flip the inequality): $$x

What is a closed circle on a number line?

A closed circle indicates that the number is included in the solution set (e.g., $$x \\le 5$$ ).

What is an open circle on a number line?

An open circle indicates that the number is not included in the solution set (e.g., $$x

How do you graph the solution to $$x > 2$$ ?

Draw a number line, place an open circle at 2, and shade to the right to indicate all values greater than 2.

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

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

What does the inequality $$x + 4

To solve, subtract 4 from both sides: $$x

How do you check if a number is a solution to an inequality?

Substitute the number into the inequality. If the statement is true, then the number is a solution.

What is the solution to the inequality $$3x - 5 > 4$$ ?

Add 5 to both sides: $$3x > 9$$ . Then divide by 3: $$x > 3$$ .

What does the graph of $$x > 3$$ look like?

The graph of $$x > 3$$ is a number line with an open circle at 3 and shading to the right, indicating all values greater than 3.

5-1 to 5-3 Check In Flashcards

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1.

FLASHCARD QUESTION

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, or not equal to the other. Examples include <, >, ≤, and ≥.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the significance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign is necessary because multiplying or dividing both sides of an inequality by a negative number reverses the order of the inequality.

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