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 7k - 2 ≥ -9?

Back

Add 2 to both sides: 7k ≥ -7. Then divide by 7: k ≥ -1.

Front

What does the inequality 71 - 3.5x < 50 represent in a real-world context?

Back

It represents the time it takes for the temperature in the ice rink to fall below 50°F, where x is the number of hours.

Front

What is the first step to solve the inequality -12x + 1 > -47?

Back

Subtract 1 from both sides: -12x > -48.

Front

What is the solution to the inequality 10x + 300 ≥ 2000?

Back

Subtract 300 from both sides: 10x ≥ 1700. Then divide by 10: x ≥ 170.

Front

What does the symbol '≥' mean in an inequality?

Back

It means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to the number.

Front

How can you check if your solution to an inequality is correct?

Back

You can substitute the solution back into the original inequality to see if it holds true.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

If x < 4, what are some possible values for x?

Back

Possible values include 3, 2, 1, 0, -1, etc.

Front

What is the process to graph the inequality x < 4 on a number line?

Back

Draw a number line, place an open circle on 4, and shade to the left to indicate all numbers less than 4.