12/3 SOTW Multi-step Inequalities

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, or division.

Front

How do you solve the inequality 4(2a + 3) < 3(a - 1)?

Back

First, distribute: 8a + 12 < 3a - 3. Then, subtract 3a from both sides: 5a + 12 < -3. Next, subtract 12: 5a < -15. Finally, divide by 5: a < -3.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to another value.

Front

Solve the inequality -3(9 + x) ≥ -21.

Back

Distribute: -27 - 3x ≥ -21. Add 27 to both sides: -3x ≥ 6. Divide by -3 (remember to flip the inequality): x ≤ -2.

Front

What is the solution to the inequality 6x + 10 > 5x - 12?

Back

Subtract 5x from both sides: x + 10 > -12. Then, subtract 10: x > -22.

Front

How do you interpret the solution k ≤ 7?

Back

This means that k can be any number that is less than or equal to 7.

Front

What is the first step in solving the inequality 28 - k ≥ 7(k - 4)?

Back

First, distribute on the right side: 28 - k ≥ 7k - 28.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, often resulting from contradictory statements.

Front

What is the difference between '>' and '<' in inequalities?

Back

'>' means 'greater than', while '<' means 'less than'. They indicate the direction of the comparison between two values.

Front

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

Back

Substitute the solution back into the original inequality to see if it holds true.