2 step inequalities

Front

What is a 2-step inequality?

Back

A 2-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 11 > -3y + 2?

Back

First, subtract 2 from both sides: 11 - 2 > -3y, which simplifies to 9 > -3y. Then, divide by -3 and flip the inequality sign: -3 < y.

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 7n - 1 > 76.

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

Front

Solve the inequality -2x - 3 ≤ 13.

Back

Add 3 to both sides: -2x ≤ 16. Then divide by -2 and flip the sign: x ≥ -8.

Front

Solve the inequality 3x + 7 < 22.

Back

Subtract 7 from both sides: 3x < 15. Then divide by 3: x < 5.

Front

What does it mean if an inequality is 'open'?

Back

An open inequality means that the variable can take on values that do not include the boundary point, indicated by < or >.

Front

What does it mean if an inequality is 'closed'?

Back

A closed inequality means that the variable can take on values that include the boundary point, indicated by ≤ or ≥.

Front

Graph the inequality x < 3.

Back

Draw a number line, place an open circle at 3, and shade to the left to indicate all numbers less than 3.

Front

What is the solution set for the inequality 4x + 1 > 9?

Back

Subtract 1 from both sides: 4x > 8. Then divide by 4: x > 2.