Solving and graphing two-step inequalities

Front

What is a two-step inequality?

Back

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 -3 - 6(4x + 6) > -111?

Back

First, distribute: -3 - 24x - 36 > -111. Combine like terms: -24x - 39 > -111. Add 39 to both sides: -24x > -72. Divide by -24 (flip the sign): x < 3.

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 for f: 23 < f - 12.

Back

Add 12 to both sides: 35 < f, or f > 35.

Front

What is the solution to the inequality 6n + 4 > -26?

Back

Subtract 4 from both sides: 6n > -30. Divide by 6: n > -5.

Front

How do you graph the inequality 2k - 9 ≤ -19?

Back

First, solve for k: 2k ≤ -10, k ≤ -5. Graph with a closed circle at -5, shading to the left.

Front

What is the difference between a closed circle and an open circle on a graph?

Back

A closed circle indicates that the number is included in the solution (≤ or ≥), while an open circle indicates it is not included (< or >).

Front

What is the first step in solving the inequality -3x ≥ 12?

Back

Divide both sides by -3, remembering to flip the inequality sign: x ≤ -4.

Front

What does 'combining like terms' mean?

Back

It means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power.

Front

What is the solution to the inequality 5x + 2 < 17?

Back

Subtract 2 from both sides: 5x < 15. Divide by 5: x < 3.