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 = 11, you would first subtract 3 and then divide by 2 to find x.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. For example, x < 5 means x is less than 5.

Front

How do you solve a two-step equation?

Back

To solve a two-step equation, isolate the variable by performing inverse operations in the reverse order of operations. For example, in 3x + 4 = 10, subtract 4 from both sides, then divide by 3.

Front

What does it mean to 'isolate the variable'?

Back

Isolating the variable means to manipulate the equation so that the variable is on one side of the equation by itself, making it easier to solve.

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.

Front

What is the maximum number of friends Dylon can take to the movies if he has $50 and adult tickets cost $9.75?

Back

Dylon can take a maximum of 6 friends, as the total cost for 1 adult and 6 children is $50.

Front

How do you set up an inequality for a word problem?

Back

Identify the total amount available and the costs involved, then express the relationship using an inequality. For example, if you have $10 to spend and each item costs $3, the inequality would be 3x ≤ 10.

Front

What is the total cost of Terry's car repair if he was charged $50 per hour for 4.5 hours?

Back

The total cost is $375, calculated as (4.5 hours * $50) + $150 for parts.

Front

How do you represent a situation where you want to spend no more than a certain amount?

Back

You can represent this with an inequality. For example, if you want to spend no more than $10, you would write the inequality as total cost ≤ $10.

Front

What is the cost of each candy bar if Keith spent $14 total, buying 1 soft drink for $2 and 6 candy bars?

Back

Each candy bar costs $2, calculated as (14 - 2) / 6.