Solving Inequalities

Front

What is an inequality?

Back

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

Front

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

Back

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

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

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

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is greater than or equal to 2.

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

How do you solve the inequality -4(5x + 3) - 6x > 11 - 3x?

Back

First, distribute -4: -20x - 12 - 6x > 11 - 3x. Combine like terms: -26x - 12 > 11 - 3x. Then isolate x to find x < -1.

Front

What is the first step to solve the inequality a - 6 ≤ 15 + 8a?

Back

The first step is to add 6 to both sides: a ≤ 21 + 8a.

Front

How do you write 'You spend less than 2 hours on homework' as an inequality?

Back

It can be written as x < 2, where x represents the hours spent on homework.

Front

What is the solution to the inequality -10x + 5 ≥ 195?

Back

To solve, subtract 5 from both sides: -10x ≥ 190. Then divide by -10 (remember to flip the inequality): x ≤ -19.

Front

What does it mean to isolate the variable in an inequality?

Back

Isolating the variable means to get the variable (like x or a) on one side of the inequality by itself.