Two-Step Equations & Inequalities Word Problems Flashcard

Front

What is a two-step equation?

Back

A two-step equation is an algebraic equation that requires two operations to solve for the variable. For example, in the equation 2x + 3 = 7, you would first subtract 3 and then divide by 2 to find x.

Front

What does it mean to solve an inequality?

Back

Solving an inequality involves finding the values of a variable that make the inequality true. For example, in the inequality x + 5 > 10, you would subtract 5 from both sides to find x > 5.

Front

How do you represent a word problem as an equation?

Back

To represent a word problem as an equation, identify the quantities involved, assign variables, and translate the relationships described in the problem into mathematical expressions.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

How do you isolate a variable in a two-step equation?

Back

To isolate a variable in a two-step equation, perform the inverse operations in reverse order. First, eliminate the constant term, then divide or multiply to solve for the variable.

Front

What is the first step in solving the equation 50 + 20m = 290?

Back

The first step is to subtract 50 from both sides of the equation to isolate the term with the variable: 20m = 240.

Front

How do you write an inequality for a maximum value problem?

Back

To write an inequality for a maximum value problem, express the total amount and set it less than or equal to the maximum limit. For example, if you have a budget of $10, you would write the inequality as total cost ≤ 10.

Front

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

Back

The symbol '≥' means 'greater than or equal to.' It indicates that the value on the left is either greater than or equal to the value on the right.

Front

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

Back

To check if your solution to an inequality is correct, substitute the solution back into the original inequality and verify if the statement holds true.

Front

What is a real-world example of a two-step inequality?

Back

A real-world example of a two-step inequality is budgeting for expenses. If you have $50 and spend $10 on a meal, you can write the inequality 50 - 10x ≥ 0 to find out how many meals you can afford.