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 represent a situation where you want to spend at most a certain amount of money?

Back

You can represent this situation using an inequality, such as 'x ≤ amount', where x is the variable representing the total cost.

Front

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

Back

The symbol '<' means 'less than', indicating that the value on the left side is smaller than the value on the right side.

Front

How do you solve the inequality 12x + 400 < 1200 for x?

Back

First, subtract 400 from both sides to get 12x < 800. Then, divide both sides by 12 to find x < 66.67.

Front

What is the first step in solving the inequality 2.50x + 5 ≤ 20?

Back

The first step is to subtract 5 from both sides, resulting in 2.50x ≤ 15.

Front

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

Back

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

Front

How do you isolate the variable in the inequality -3 - 6(4x + 6) > -111?

Back

First, distribute -6 to get -3 - 24x - 36 > -111. Then, combine like terms and isolate x.

Front

What is the solution to the inequality 9 ≥ -2m + 2 - 3?

Back

First, simplify the right side to get 9 ≥ -2m - 1. Then, add 1 to both sides to get 10 ≥ -2m, and finally divide by -2, reversing the inequality to get m ≥ -5.

Front

What is the importance of reversing the inequality sign when dividing by a negative number?

Back

Reversing the inequality sign is crucial because it maintains the true relationship between the values when both sides of the inequality are multiplied or divided by a negative number.

Front

What is a real-world example of a multistep inequality?

Back

A real-world example is budgeting for expenses, such as determining how much you can spend on groceries each week while staying within a monthly budget.