Multi-Step 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 operations such as addition, subtraction, multiplication, or division on both sides.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable in an inequality, perform inverse operations on both sides of the inequality, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Tags

CCSS.6.EE.B.8

Front

What does it mean to graph the solution set of an inequality?

Back

Graphing the solution set of an inequality involves representing all possible solutions on a number line, using open or closed circles to indicate whether endpoints are included.

Tags

CCSS.6.EE.B.8

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the endpoint, while a non-strict inequality (e.g., ≤ or ≥) includes the endpoint.

Tags

CCSS.6.EE.B.8

Front

How do you solve the inequality -4a ≤ -28?

Back

To solve -4a ≤ -28, divide both sides by -4, which reverses the inequality sign, resulting in a ≥ 7.

Tags

CCSS.6.EE.B.8

Front

What is the solution to the inequality 4(2a + 3) < 3(a - 1)?

Back

To solve 4(2a + 3) < 3(a - 1), first distribute: 8a + 12 < 3a - 3. Then, subtract 3a from both sides: 5a + 12 < -3. Finally, subtract 12 and divide by 5 to get a < -3.

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How do you solve the inequality 14 < -2a + 6 - 2a?

Back

Combine like terms: 14 < -4a + 6. Subtract 6 from both sides: 8 < -4a. Divide by -4 (reversing the inequality) to get a < -2.

Front

What is the solution to the inequality x ≤ -28/3?

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The solution x ≤ -28/3 indicates that x can take any value less than or equal to -28/3.

Tags

CCSS.6.EE.B.8

Front

What is the importance of checking your solution in an inequality?

Back

Checking your solution in an inequality ensures that the values satisfy the original inequality, confirming that the solution is correct.

Front

What is the role of parentheses and brackets in graphing inequalities?

Back

Parentheses indicate that the endpoint is not included (open circle), while brackets indicate that the endpoint is included (closed circle) in the graph of the inequality.

Tags

CCSS.6.EE.B.8