Two-Step Inequality Word Problems

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, often involving addition or subtraction followed by multiplication or division.

Front

How do you write an inequality for a word problem?

Back

Identify the variable, determine the relationship (greater than, less than, etc.), and translate the words into a mathematical expression.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

In the problem, 'Elliott has $50 and spends $9.75 on an adult ticket and $6.25 on each child ticket', how do you define the variable?

Back

Let x = the number of child tickets Elliott buys.

Front

What is the first step to solve the inequality 6.25x + 9.75 ≤ 50?

Back

Subtract 9.75 from both sides to isolate the term with x.

Front

What is the solution to the inequality 50x + 2400 ≥ 4800?

Back

x ≥ 48, meaning Jillian needs to save for at least 48 weeks.

Front

How do you interpret the solution x ≥ 28 in the context of Ruby's savings goal?

Back

Ruby needs to save for at least 28 weeks to reach her goal of $200.

Front

What is the importance of defining a variable in a word problem?

Back

Defining a variable helps to clarify what you are solving for and makes it easier to set up the inequality.

Front

In the context of Emilia's problem, how do you set up the inequality?

Back

Let x = the number of cars washed; the inequality is 14x + 30 ≥ 240.