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. Remember to reverse the inequality sign when multiplying or dividing by a negative number.

Tags

CCSS.6.EE.B.8

Front

What does it mean for one boarding option to be less expensive than another in terms of inequalities?

Back

It means that the cost function of one option must be less than the cost function of the other option, which can be represented as an inequality.

Tags

CCSS.6.EE.B.8

Front

In the context of Jake's dog boarding problem, how do you set up the inequality?

Back

You set up the inequality by comparing the total costs of both boarding houses: 90 + 5d < 100 + 4d, where d is the number of days.

Tags

CCSS.7.EE.B.4B

Front

What is the solution to the inequality 90 + 5d < 100 + 4d?

Back

The solution is d < 10, meaning Jake must board his dog for less than 10 days for house A to be cheaper.

Front

What is the first step in solving the inequality 14 + 9x > 6x + 4?

Back

The first step is to isolate the variable x by subtracting 6x from both sides, resulting in 14 + 3x > 4.

Front

What is the solution to the inequality 14 + 9x > 6x + 4?

Back

The solution is x > -3 1/3.

Front

How do you interpret the solution k < 0 in the inequality 8 - 3k < 8(1 - 7k)?

Back

It means that k must be a negative number for the inequality to hold true.

Front

What does the inequality 12(2x + 3) ≤ 4(2x - 7) represent?

Back

It represents a condition where the left side, when simplified, must be less than or equal to the right side.

Front

What is the solution to the inequality 12(2x + 3) ≤ 4(2x - 7)?

Back

The solution is x ≤ -4.