Solving Inequalities

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 an inequality?

Back

The symbol '>' means 'greater than'. For example, 6 > x means 6 is greater than x.

Front

What does the symbol '<' mean in an inequality?

Back

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

Front

How do you solve the inequality 8x - 10 = -34?

Back

Add 10 to both sides to get 8x = -24, then divide by 8 to find x = -3.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is less than or equal to 4.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 3 means x is greater than or equal to 3.

Front

How do you graph the inequality x > -5?

Back

Draw a number line, place an open circle at -5, and shade to the right to indicate all numbers greater than -5.

Front

How do you write an inequality for 'twenty-two more than four times a number is less than 82'?

Back

The inequality is 22 + 4n < 82.

Front

What is the solution to the inequality -2(x + 2) < 14?

Back

First, divide by -2 (remember to flip the inequality): x + 2 > -7, then subtract 2 to find x > -9.

Front

What is the solution set for the inequality 11 ≤ a?

Back

The solution set includes all values of a that are 11 or greater.