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 combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality -2(5 + 6n) < 6(8 - 2n)?

Back

First, distribute -2 and 6, then combine like terms and isolate n. The solution is infinite solutions.

Front

What does the solution 'h ≤ 2' represent in the inequality -5h + 2 ≥ -8?

Back

It means that h can take any value less than or equal to 2.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable, perform inverse operations on both sides of the inequality, similar to solving an equation, while remembering to reverse the inequality sign if multiplying or dividing by a negative number.

Front

What is the first step in solving the inequality 3 < -5n + 2n?

Back

Combine like terms on the right side to simplify the inequality to 3 < -3n.

Front

What does the inequality 12x + 400 < 1200 represent in a real-world context?

Back

It represents a budget constraint where the total monthly payments (12x) plus a down payment (400) must be less than $1200.

Front

What is the solution to the inequality 6x + 2 < 14?

Back

First, subtract 2 from both sides to get 6x < 12, then divide by 6 to find x < 2.

Front

What is the significance of the inequality sign in solving inequalities?

Back

The inequality sign indicates the relationship between two expressions and determines the range of possible solutions for the variable.

Front

What happens to the inequality sign when you multiply or divide both sides by a negative number?

Back

The inequality sign reverses direction when you multiply or divide both sides by a negative number.

Front

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

Back

You can check your solution by substituting a value from the solution set back into the original inequality to see if it holds true.