2 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. For example, in the inequality 2x + 3 < 7, you would first subtract 3 from both sides and then divide by 2.

Front

How do you solve the inequality -3x ≤ 18?

Back

To solve -3x ≤ 18, divide both sides by -3, which reverses the inequality sign: x ≥ -6.

Front

What does the inequality 11 > -3y + 2 mean?

Back

This means that -3y + 2 is less than 11. To solve, subtract 2 from both sides to get -3y < 9, then divide by -3 to find y > -3.

Front

When do you use an open circle on a graph for an inequality?

Back

An open circle is used when the inequality is > or <, indicating that the endpoint is not included in the solution.

Front

What does the inequality x < 6 represent on a number line?

Back

It represents all numbers less than 6, with an open circle at 6 to indicate that 6 is not included.

Front

How do you graph the inequality 7n - 1 > 76?

Back

First, solve for n: 7n > 77, then n > 11. Graph with an open circle at 11 and shade to the right.

Front

What is the difference between ≤ and < in inequalities?

Back

≤ means 'less than or equal to' and includes the endpoint, while < means 'less than' and does not include the endpoint.

Front

What does it mean to reverse the inequality sign?

Back

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

Front

How do you interpret the solution of an inequality?

Back

The solution of an inequality represents a range of values that satisfy the inequality, often expressed in interval notation.

Front

What is interval notation for x ≥ -6?

Back

The interval notation is [-6, ∞), indicating that -6 is included and extends to positive infinity.