Inequalities and Systems Review

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 in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is greater than 3.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 5 means x is less than 5.

Front

How do you solve the inequality -3 - 6(4x + 6) > -111?

Back

First, simplify: -3 - 24x - 36 > -111. Then combine like terms: -24x - 39 > -111. Add 39 to both sides: -24x > -72. Finally, divide by -24 (remember to flip the inequality): x < 3.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the inequality that models the taxi fare scenario: $2.50 per mile plus a $5 fee, not exceeding $20?

Back

The inequality is 2.50x + 5 ≤ 20, where x is the number of miles.

Front

How do you set up an inequality for a budget scenario?

Back

Identify the total cost and set it less than or equal to the budget. For example, if you have a $1200 budget and a $400 down payment, the inequality is 12x + 400 ≤ 1200.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, b ≥ 5 means b is greater than or equal to 5.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 10 means x is less than or equal to 10.