Solve Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Tags

CCSS.6.EE.B.8

Front

How do you solve the inequality 2x + 6 ≥ -8?

Back

To solve 2x + 6 ≥ -8, first subtract 6 from both sides to get 2x ≥ -14, then divide both sides by 2 to find x ≥ -7.

Tags

CCSS.7.EE.B.4B

Front

What is the first step in solving the inequality -4x + 14 ≤ 54?

Back

The first step is to subtract 14 from both sides, resulting in -4x ≤ 40.

Tags

CCSS.7.EE.B.4B

Front

What does the solution x < -20 represent on a number line?

Back

The solution x < -20 represents all numbers to the left of -20 on a number line, not including -20 itself.

Tags

CCSS.6.EE.B.8

Front

How do you graph the inequality 3 + 9k > 111?

Back

First, solve for k: 9k > 108, then k > 12. On a number line, draw an open circle at 12 and shade to the right.

Tags

CCSS.6.EE.B.8

Front

What is the solution to the inequality 7n - 1 > 76?

Back

To solve 7n - 1 > 76, add 1 to both sides to get 7n > 77, then divide by 7 to find n > 11.

Tags

CCSS.7.EE.B.4B

Front

What does it mean if an inequality is written with a 'greater than or equal to' symbol (≥)?

Back

It means that the variable can take on values that are greater than or equal to a certain number.

Tags

CCSS.6.EE.B.8

Front

What is the difference between 'greater than' (>) and 'greater than or equal to' (≥)?

Back

'Greater than' (>) means the value cannot equal the number, while 'greater than or equal to' (≥) includes the number itself as a possible solution.

Tags

CCSS.6.EE.B.8

Front

How do you check your solution for an inequality?

Back

To check your solution, substitute the value back into the original inequality to see if it makes the inequality true.

Tags

CCSS.6.EE.B.8

Front

What is the importance of reversing the inequality sign when multiplying or dividing by a negative number?

Back

Reversing the inequality sign is necessary to maintain the truth of the inequality when multiplying or dividing both sides by a negative number.

Tags

CCSS.6.EE.B.8