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 with an inequality, such as x ≤ amount, where x is the total cost.

Front

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

Back

The symbol '>' means 'greater than'.

Front

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

Back

The symbol '<' means 'less than'.

Front

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

Back

Subtract 400 from both sides to get 12x < 800, then divide by 12 to find x < 66.67.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

The solution is x ≥ -10.

Front

How do you graph the inequality r ≥ -6?

Back

You would draw a solid dot on -6 and shade to the right, indicating all values greater than or equal to -6.

Front

What is the first step to solve the inequality -p - 4p > -10?

Back

Combine like terms to get -5p > -10.

Front

What does it mean if an inequality has a solid dot on a number line?

Back

A solid dot indicates that the number is included in the solution (≥ or ≤).

Front

What does it mean if an inequality has an open dot on a number line?

Back

An open dot indicates that the number is not included in the solution (> or <).