Solving multistep inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving multiple operations such as addition, subtraction, multiplication, or division.

Front

What is the first step in solving the inequality \( \frac{x}{-6} + 20 > 4 \)?

Back

The first step is to undo the addition by subtracting 20 from both sides.

Front

What operations must be undone to solve the inequality \( 9x - 6 > 66 \)?

Back

You must first undo the subtraction by adding 6 to both sides, then divide by 9.

Front

When solving inequalities, what happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign must be reversed when you multiply or divide both sides of the inequality by a negative number.

Front

What is the first step to solve the inequality \( \frac{m}{-6} + 17 \le 23 \)?

Back

The first step is to subtract 17 from both sides of the inequality.

Front

How do you isolate the variable in the inequality \( 9 - \frac{4}{5}x \le -3 \)?

Back

First, subtract 9 from both sides, then multiply both sides by -\frac{5}{4} and reverse the inequality sign.

Front

What is the importance of reversing the inequality sign?

Back

Reversing the inequality sign is crucial when multiplying or dividing by a negative number to maintain the truth of the inequality.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you check if a value is a solution to an inequality?

Back

To check if a value is a solution, substitute it into the inequality and see if the statement is true.

Front

What does it mean to 'undo' an operation in solving inequalities?

Back

To 'undo' an operation means to perform the inverse operation to isolate the variable.