Solving and graphing 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. It often involves 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 (remember to flip the inequality): -3 < y.

Front

What does the inequality x + 134 ≤ 400 represent?

Back

It represents the maximum number of people that can enter a room if there are already 134 people inside and the room can hold a maximum of 400 people.

Front

What is the solution to the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides: 2k ≤ -10. Then divide by 2: k ≤ -5.

Front

What does a closed circle on a number line indicate?

Back

A closed circle indicates that the number is included in the solution set (≤ or ≥).

Front

What does an open circle on a number line indicate?

Back

An open circle indicates that the number is not included in the solution set (< or >).

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 first step in solving the inequality 6n + 4 > -26?

Back

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

Front

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

Back

n > -5.

Front

What is the difference between ≤ and < in inequalities?

Back

≤ means 'less than or equal to' (includes the number), while < means 'less than' (does not include the number).