Algebra 1 RQ2**

Front

What is the equation to find the hourly rate of a phone plan if there is a sign-up fee and a charge per hour?

Back

The equation is: Total Cost = Sign-up Fee + (Hourly Rate * Number of Hours). For example, if the sign-up fee is $3.50 and the total cost is $75.50 for 12 hours, the equation is: 3.50 + 12x = 75.50.

Front

How do you solve the inequality -2x - 3 < 9?

Back

To solve -2x - 3 < 9, first add 3 to both sides: -2x < 12. Then divide by -2 (remember to flip the inequality sign): x > -6.

Front

What inequality represents the maximum weight a truck can carry if it is loaded with a piano and boxes?

Back

The inequality is: Weight of Piano + (Weight of Each Box * Number of Boxes) ≤ Maximum Weight. For example, if the piano weighs 400 pounds and each box weighs 50 pounds, the inequality is: 50x + 400 ≤ 1600.

Front

How do you solve the inequality -6x - 8 > -32?

Back

To solve -6x - 8 > -32, first add 8 to both sides: -6x > -24. Then divide by -6 (remember to flip the inequality sign): x < 4.

Front

What does the inequality x/8 > 4 represent?

Back

The inequality x/8 > 4 means that x must be greater than 32. To solve, multiply both sides by 8: x > 32.

Front

What is the significance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign is necessary because it changes the direction of the relationship between the two sides of the inequality.

Front

What is a sign-up fee in a phone plan?

Back

A sign-up fee is a one-time charge that a customer pays when they start a service, in addition to any ongoing charges.

Front

How do you represent a situation with multiple variables in an inequality?

Back

You can represent a situation with multiple variables in an inequality by combining the variables and constants in a way that reflects the constraints of the situation.

Front

What is the process for solving a linear inequality?

Back

The process for solving a linear inequality involves isolating the variable on one side of the inequality, using inverse operations, and remembering to flip the inequality sign when multiplying or dividing by a negative number.

Front

What does it mean for a solution to an inequality to be 'all possible values'?

Back

It means that the solution set includes every value that satisfies the inequality, often represented as an interval or range.