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 such as addition, subtraction, multiplication, or division.

Front

How do you isolate a variable in a multi-step inequality?

Back

To isolate a variable, perform inverse operations on both sides of the inequality, ensuring to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What does the symbol '>' represent in inequalities?

Back

'>' means 'greater than', indicating that the value on the left is larger than the value on the right.

Front

What does the symbol '≥' represent in inequalities?

Back

'≥' means 'greater than or equal to', indicating that the value on the left is either larger than or equal to the value on the right.

Front

What does the symbol '≤' represent in inequalities?

Back

'≤' means 'less than or equal to', indicating that the value on the left is either smaller than or equal to the value on the right.

Front

How do you graph a solution to an inequality on a number line?

Back

To graph an inequality, use an open circle for '>' or '<' and a closed circle for '≥' or '≤'. Shade the region that represents the solution set.

Front

What is the first step in solving the inequality -4x + 14 ≤ 54?

Back

The first step is to isolate the term with the variable by subtracting 14 from both sides, resulting in -4x ≤ 40.

Front

What is the final solution for the inequality -4x + 14 ≤ 54?

Back

The final solution is x ≥ -10 after dividing both sides by -4 and reversing the inequality sign.

Front

What is the importance of checking your solution in an inequality?

Back

Checking your solution ensures that the values satisfy the original inequality, confirming that the solution is correct.

Front

What is a compound inequality?

Back

A compound inequality consists of two or more inequalities joined by 'and' or 'or', representing a range of values.