Inequalities Word Problems

Front

What is an inequality?

Back

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

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

How do you represent a situation where a number must be less than a certain value?

Back

You can represent it using an inequality, for example, x < 10 means x must be less than 10.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

Front

How do you solve the inequality -4x + 2 < 10?

Back

First, subtract 2 from both sides: -4x < 8. Then, divide by -4 (remember to flip the inequality): x > -2.

Front

What is the solution to the inequality 1.75t + 3.50 ≤ 20?

Back

To solve, subtract 3.50 from both sides: 1.75t ≤ 16.50. Then divide by 1.75: t ≤ 9.43.

Front

What does it mean if a child must be no more than 62 inches tall to play?

Back

It means the child's height must satisfy the inequality k ≤ 62.

Front

How do you solve the inequality -2(x - 5) < 4?

Back

Distribute -2: -2x + 10 < 4. Then, subtract 10: -2x < -6. Finally, divide by -2 (flip the inequality): x > 3.

Front

What is the inequality that represents a budget of $20 for tacos costing $1.75 each after spending $3.50 on drinks?

Back

The inequality is 1.75t + 3.50 ≤ 20.