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 operations such as addition, subtraction, multiplication, or division.

Front

How do you isolate a variable in an inequality?

Back

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

Front

What does the inequality symbol '≥' mean?

Back

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

Front

What does the inequality symbol '≤' mean?

Back

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

Front

How do you graph a solution to an inequality?

Back

To graph a solution to an inequality, use a number line: 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 9 ≥ -2m + 2 - 3?

Back

The first step is to simplify the right side of the inequality by combining like terms, resulting in 9 ≥ -2m - 1.

Front

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

Back

First, distribute -6 to both terms inside the parentheses, then combine like terms and isolate x by performing inverse operations.

Front

What is the purpose of using inequalities in real-life scenarios?

Back

Inequalities are used in real-life scenarios to represent constraints or limits, such as budgets, capacities, and maximum or minimum requirements.

Front

How can you represent a budget constraint using an inequality?

Back

A budget constraint can be represented using an inequality by setting up an expression that includes all expenses and ensuring it does not exceed the total budget.

Front

What is the solution to the inequality 2.50x + 5 ≤ 20?

Back

To solve for x, subtract 5 from both sides to get 2.50x ≤ 15, then divide by 2.50 to find x ≤ 6.