How do you solve the inequality $$2(x - 3) - 5x ≤ 9$$ ?

First, distribute: $$2x - 6 - 5x ≤ 9$$ . Combine like terms: $$-3x - 6 ≤ 9$$ . Add 6 to both sides: $$-3x ≤ 15$$ . Divide by -3 (remember to flip the inequality): $$x ≥ -5$$ .

What is the solution to the inequality $$8m + 0.15(760) ≥ 760$$ ?

First, calculate $$0.15(760) = 114$$ . Then, the inequality becomes $$8m + 114 ≥ 760$$ . Subtract 114 from both sides: $$8m ≥ 646$$ . Divide by 8: $$m ≥ 80.75$$ .

What is the first step in solving a multi-step inequality?

The first step is to simplify both sides of the inequality if possible, by distributing and combining like terms.

How do you check the solution of an inequality?

To check the solution, substitute a value from the solution set back into the original inequality to see if it holds true.

What does it mean if an inequality has no solution?

It means that there are no values that can satisfy the inequality. For example, $$x

What is the relationship between inequalities and graphs?

Inequalities can be represented on a number line, where a closed dot indicates inclusion (≤ or ≥) and an open dot indicates exclusion ( ).

How do you write an inequality from a word problem?

Identify the quantities involved and their relationships. For example, if a problem states that a person can spend no more than $40, you can write $$x ≤ 40$$ , where x is the amount spent.

What is the importance of understanding inequalities in real life?

Understanding inequalities helps in making decisions based on constraints, such as budgeting, resource allocation, and planning.

How do you solve for a variable in an inequality?

Isolate the variable on one side of the inequality by performing inverse operations, similar to solving an equation.

What does it mean to have a variable in an inequality?

A variable in an inequality represents an unknown quantity that can take on different values, affecting the outcome of the inequality.

Lesson 17 Flashcard Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an inequality?

Back

Tags

CCSS.6.EE.B.8

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What does it mean to raise funds equally among a group?

Back

Tags

CCSS.5.NF.B.3

4.

FLASHCARD QUESTION

Front

How do you set up an inequality for a budget problem?

Back

Tags

CCSS.7.EE.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.7.EE.B.4B

6.

FLASHCARD QUESTION

Front

What is the significance of the solution to an inequality?

Back

7.

FLASHCARD QUESTION

Front

Back

This means that the maximum value of x is 3. In a shopping scenario, if x represents the number of items Lydia can buy, she can buy at most 3 items.

Tags

CCSS.6.EE.B.8

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