Solving Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you solve the inequality 2x - 3 ≥ 4x - 1?

Back

Rearranging gives -3 + 1 ≥ 4x - 2x, which simplifies to -2 ≥ 2x, or x ≤ -1.

Front

What is the solution to the inequality x + 4 ≤ -18?

Back

Subtracting 4 from both sides gives x ≤ -22.

Front

What does the inequality x < -2 represent on a number line?

Back

It represents all numbers to the left of -2, not including -2 itself.

Front

How do you graph the inequality x > -9?

Back

Draw a number line, place an open circle at -9, and shade to the right.

Front

What is the solution to the inequality -2x + 2 > 3x - 8?

Back

Rearranging gives 2 + 8 > 3x + 2x, which simplifies to 10 > 5x, or x < 2.

Front

What is the solution to the inequality 3x - 2 < 13?

Back

Adding 2 to both sides gives 3x < 15, then dividing by 3 gives x < 5.

Front

What does the inequality x ≥ 1 mean?

Back

It means x can be 1 or any number greater than 1.