Writing Inequalities from Word Problems

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

How do you represent a word problem as an inequality?

Back

Identify the quantities involved, 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 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

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

Front

In the inequality 5x + 10 ≥ 100, what does 'x' represent?

Back

'x' represents the number of hours Joan needs to babysit.

Front

How do you solve the inequality 5x + 10 ≥ 100 for x?

Back

Subtract 10 from both sides to get 5x ≥ 90, then divide by 5 to find x ≥ 18.

Front

What is the maximum number of hours the DJ can play if 125x + 55 < 600?

Back

To find the maximum hours, solve for x: 125x < 545, so x < 4.36 hours.

Front

What does the phrase 'at least' indicate in an inequality?

Back

The phrase 'at least' indicates that the value can be equal to or greater than a certain number, represented by '≥'.

Front

In the inequality 4x + 7 ≥ 19, how do you isolate x?

Back

Subtract 7 from both sides to get 4x ≥ 12, then divide by 4 to find x ≥ 3.

Front

What does the inequality 6 + x ≤ 35 represent?

Back

It represents that the total height of the tree (currently 6 feet plus growth x) cannot exceed 35 feet.