Linear inequalities (one variable)

Front

What is a linear inequality in one variable?

Back

A linear inequality in one variable is an inequality that can be expressed in the form ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c, where a, b, and c are constants and x is the variable.

Tags

CCSS.7.EE.B.4B

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality by performing inverse operations, 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 the solution x > 9 represent in a linear inequality?

Back

The solution x > 9 represents all real numbers greater than 9, meaning any value of x that is more than 9 satisfies the inequality.

Tags

CCSS.6.EE.B.8

Front

What is the first step in solving the inequality 2x + 3y < 6 for y?

Back

The first step is to isolate y by subtracting 2x from both sides, resulting in 3y < 6 - 2x.

Front

How do you interpret the inequality 90 + 5x < 100 + 4x in a real-world context?

Back

This inequality compares the total cost of boarding a dog at two different boarding houses, where x represents the number of days the dog is boarded.

Tags

CCSS.7.EE.B.4B

Front

What is the solution to the inequality -4x + 10 < 6x - 10?

Back

The solution is x > 2, meaning any value of x greater than 2 satisfies the inequality.

Front

What does the inequality x < -2 indicate?

Back

The inequality x < -2 indicates that x can take any value less than -2, which includes all negative numbers that are less than -2.

Tags

CCSS.6.EE.B.8

Front

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

Back

Reversing the inequality sign is crucial because it maintains the truth of the inequality; for example, if you multiply both sides of an inequality by -1, the direction of the inequality must change.

Tags

CCSS.6.EE.B.8

Front

How can you graph the solution x > 9 on a number line?

Back

To graph x > 9 on a number line, draw an open circle at 9 (indicating that 9 is not included) and shade the line to the right to represent all numbers greater than 9.

Tags

CCSS.6.EE.B.8

Front

What is the difference between strict inequalities (<, >) and inclusive inequalities (≤, ≥)?

Back

Strict inequalities (<, >) do not include the boundary value, while inclusive inequalities (≤, ≥) do include the boundary value in the solution set.

Tags

CCSS.6.EE.B.8