Solving 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 combining like terms, distributing, and isolating the variable.

Front

How do you represent a situation where you want to spend at most a certain amount?

Back

You can represent this situation using an inequality, such as 'x ≤ amount' or 'total cost ≤ budget'.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left can be either greater than or equal to the value on the right.

Front

How do you solve the inequality 12x + 400 < 1200 for x?

Back

First, subtract 400 from both sides to get 12x < 800. Then, divide both sides by 12 to find x < 66.67.

Front

What is the first step in solving the inequality 6x + 10 > 5x - 12?

Back

The first step is to isolate the variable by subtracting 5x from both sides, resulting in x + 10 > -12.

Front

What does the solution x ≤ 24 represent in a real-world context?

Back

It represents that the value of x cannot exceed 24, which could relate to a limit on quantity, time, or other measurable factors.

Front

How do you graph the inequality r ≥ -6 on a number line?

Back

You would draw a closed circle on -6 (indicating that -6 is included) and shade to the right to show all values greater than -6.

Front

What is the significance of the down payment in the context of the laptop purchase inequality?

Back

The down payment reduces the total amount that needs to be financed, affecting the monthly payment calculation.

Front

How do you write an inequality to compare two cell phone plans?

Back

You can write an inequality such as '40 + 0.04x > 30 + 0.09x' to determine when one plan is more expensive than the other.

Front

What does the solution x > -22 indicate in the context of the inequality 6x + 10 > 5x - 12?

Back

It indicates that x can take any value greater than -22, which defines a range of possible solutions.