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, x > 2 means x is greater than 2.

Front

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

Back

The symbol '<' means 'less than'. For example, x < 4 means x is less than 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

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

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 5 means x is less than or equal to 5.

Front

How do you solve the inequality x + 5 > 7?

Back

Subtract 5 from both sides: x > 2.

Front

How do you solve the inequality -9x + 7 ≥ 25?

Back

Subtract 7 from both sides: -9x ≥ 18, then divide by -9 (remember to flip the inequality): x ≤ -2.

Front

If a parking garage charges $4.50 per hour, how do you express the maximum hours you can park with $18?

Back

You can park for x hours where 4.50x ≤ 18, which simplifies to x ≤ 4.

Front

What is the solution to the inequality 6 + 2h > 30?

Back

Subtract 6 from both sides: 2h > 24, then divide by 2: h > 12.

Front

What does a number line graph representing x < -4 look like?

Back

It shows an open circle at -4 and a line extending to the left.