solve multistep inequalities

Front

What is a multistep inequality?

Back

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

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 5 - 2x > 3?

Back

Subtract 5 from both sides: -2x > -2.

Front

When multiplying or dividing both sides of an inequality by a negative number, what must you do?

Back

You must reverse the inequality sign.

Front

Solve the inequality 3x - 4 ≤ 5. What is the solution?

Back

Add 4 to both sides: 3x ≤ 9. Then divide by 3: x ≤ 3.

Front

What does the solution x > 2 represent on a number line?

Back

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

Front

How do you graph the solution to the inequality x < -1?

Back

Draw a number line, place an open circle at -1, and shade to the left.

Front

What is the solution to the compound inequality 1 < 2x + 3 < 7?

Back

Subtract 3 from all parts: -2 < 2x < 4. Then divide by 2: -1 < x < 2.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the endpoint, while a non-strict inequality (≤ or ≥) does include the endpoint.

Front

How do you solve the inequality -3(x - 2) < 6?

Back

Distribute -3: -3x + 6 < 6. Then subtract 6: -3x < 0. Finally, divide by -3: x > 0.