Solving Multi-Step Inequalities

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be less than or equal to a specified number.

Front

How do you solve the inequality 2x + 3 < 11?

Back

Subtract 3 from both sides: 2x < 8. Then divide by 2: x < 4.

Front

What is the first step in solving the inequality 5x - 7 ≥ 8?

Back

Add 7 to both sides: 5x ≥ 15.

Front

What does the solution x > 5 represent on a number line?

Back

It represents all numbers greater than 5, which is shown as an open circle at 5 and a line extending to the right.

Front

How do you graph the inequality x ≤ 3?

Back

Draw a closed circle at 3 and shade to the left to indicate all numbers less than or equal to 3.

Front

What is the solution to the inequality -2x + 4 > 10?

Back

Subtract 4 from both sides: -2x > 6. Then divide by -2 (remember to flip the inequality): x < -3.

Front

Write an inequality for the statement: 'A number x is at least 10.'

Back

x ≥ 10.

Front

What is the solution to the inequality 3(x - 2) < 9?

Back

Distribute: 3x - 6 < 9. Add 6: 3x < 15. Divide by 3: x < 5.

Front

How do you solve the inequality 4x + 1 ≥ 2x + 5?

Back

Subtract 2x from both sides: 2x + 1 ≥ 5. Then subtract 1: 2x ≥ 4. Finally, divide by 2: x ≥ 2.