Solving Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 25 < X - 10?

Back

Add 10 to both sides: 25 + 10 < X, which simplifies to 35 < X or X > 35.

Front

What symbol indicates an open dot when graphing an inequality?

Back

The symbols < and > indicate an open dot when graphing an inequality.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality sign): x ≥ -10.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

Solve the inequality -3x ≥ 12. Do I need to flip my sign?

Back

Yes, divide by -3 and flip the sign: x ≤ -4.

Front

What is the solution to the inequality -4x + 1 > 21?

Back

Subtract 1 from both sides: -4x > 20. Then divide by -4 (flip the sign): x < -5.

Front

What does the symbol ≤ mean?

Back

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

Front

What does the symbol ≥ mean?

Back

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

Front

How do you graph the inequality x > 3?

Back

Draw a number line, place an open dot at 3, and shade to the right.