Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is not equal to the other.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

Write an inequality for the statement: 'We need to make at least $10,000.'

Back

x ≥ 10000

Front

How do you solve the inequality: x + 5 ≤ 13?

Back

Subtract 5 from both sides: x ≤ 8.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

When do you flip the inequality sign?

Back

You flip the inequality sign when you multiply or divide both sides of the inequality by a negative number.

Front

Solve the inequality: 3x ≥ 12.

Back

Divide both sides by 3: x ≥ 4.

Front

What is the solution to the inequality: y - 13 ≤ -15?

Back

Add 13 to both sides: y ≤ -2.

Front

What is the first step in solving an inequality?

Back

Isolate the variable by performing inverse operations (addition, subtraction, multiplication, or division) on both sides.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, often resulting from contradictory statements.