Equations and Inequalities Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

How do you represent the solution of an inequality on a number line?

Back

The solution of an inequality is represented by a line or a ray on a number line, with open circles for < or > and closed circles for ≤ or ≥.

Front

What does the inequality -2 ≤ x ≤ 5 mean?

Back

This inequality means that x can take any value from -2 to 5, including -2 and 5.

Front

How do you solve the equation (a + 3)/7 = 3?

Back

Multiply both sides by 7: a + 3 = 21. Then subtract 3 from both sides: a = 18.

Front

What is the first step to solve the inequality 0.20x + 5 ≤ 12?

Back

Subtract 5 from both sides: 0.20x ≤ 7.

Front

How do you isolate x in the inequality 0.20x ≤ 7?

Back

Divide both sides by 0.20: x ≤ 35.

Front

What does the inequality 15 + 6x ≤ 100 represent in a real-world context?

Back

It represents the maximum number of people Andrea can invite to play laser tag, given the cost structure.

Front

What is the solution to the inequality 6x + 15 ≤ 100?

Back

x ≤ 14.17, meaning Andrea can invite a maximum of 14 people.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, often resulting from contradictory statements.