M1. 4-5 Linear Inequalities in One Variable Word Problems

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥).

Front

What does the inequality symbol '≤' mean?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

How do you represent a situation where one quantity is greater than another using an inequality?

Back

You can use the '>' symbol. For example, if x is greater than 5, it is written as x > 5.

Front

What is the first step in solving a linear inequality?

Back

The first step is to isolate the variable on one side of the inequality.

Front

How do you graph a linear inequality on a number line?

Back

Use an open circle for '>' or '<' and a closed circle for '≥' or '≤'. Shade the region that satisfies the inequality.

Front

What does the phrase 'no more than' indicate in an inequality?

Back

It indicates that the value is less than or equal to a certain number, represented by '≤'.

Front

If a gym charges a joining fee and a monthly fee, how can you express the total cost after x months?

Back

Total cost = joining fee + (monthly fee × x). For example, if the joining fee is $18 and the monthly fee is $30, the total cost after x months is 18 + 30x.

Front

How do you set up an inequality to compare costs from two different gyms?

Back

Set the total cost of one gym less than or equal to the total cost of the other gym. For example, Gym A: 18 + 30x ≤ Gym B: 50 + 20x.

Front

What is the significance of the solution to a linear inequality?

Back

The solution represents all possible values of the variable that make the inequality true.

Front

How do you interpret the solution of an inequality in a real-world context?

Back

The solution indicates the range of values that satisfy the conditions of the problem, such as the number of months or items.