Two-Step Equations and Inequalities 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. It typically involves addition or subtraction followed by multiplication or division.

Front

How do you solve a two-step equation?

Back

To solve a two-step equation, isolate the variable by performing the inverse operations in reverse order: first, eliminate the constant term (add or subtract), then eliminate the coefficient of the variable (multiply or divide).

Front

What does an inequality represent?

Back

An inequality represents a relationship between two expressions that may not be equal, indicating that one is greater than, less than, greater than or equal to, or less than or equal to the other.

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 or less than another.

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 graph an inequality on a number line?

Back

To graph an inequality on a number line, use an open circle for < or > (not including the endpoint) and a closed circle for ≤ or ≥ (including the endpoint). Shade the region that represents the solution set.

Front

What is the maximum number of guests if the cost is limited to $200 for a party rental of $80 and $12.50 per guest?

Back

The maximum number of guests is 9, calculated by solving the inequality: 12.50x + 80 ≤ 200.

Front

What does the equation 4t + 109.99 = 347.95 represent?

Back

This equation represents the total cost of a trip for a family of 4, where 't' is the cost of each ticket.

Front

How do you interpret the equation 345 + 23x = 677?

Back

This equation can be interpreted as Paulina reading a book with 677 pages total, having read 345 pages, and reading 23 pages per day for 'x' days.

Front

What is the first step in solving the inequality 30x + 200 ≤ 1400?

Back

The first step is to subtract 200 from both sides to isolate the term with the variable: 30x ≤ 1200.