Application: Solving Word Problems with One-Step Inequalities
Solving word problems with one-step inequalities is a Grade 11 Algebra 1 skill from enVision Chapter 1 that applies inequality-solving to real-world constraints. Students translate verbal conditions into mathematical inequalities, solve algebraically, and interpret results in context. A car rental at /week plus /bin/zsh.20/mile with a budget gives 90 + 0.20m <= 250, so m <= 800 miles. Emma earning ,000 monthly needing income at least 4 times rent gives 6000 >= 4r, so r <= ,500. The solution represents a range of acceptable values, not a single answer.
Key Concepts
To solve linear inequality applications, translate the word problem into a mathematical inequality, then solve using algebraic properties. The key steps are: identify the variable, write the inequality from the given constraints, solve algebraically, and interpret the solution in context.
Common Questions
How do you set up an inequality from a word problem?
Identify the unknown variable, translate the constraint using inequality symbols (<=, >=, <, >), then solve algebraically and interpret in context.
A car rental costs /week plus /bin/zsh.20/mile with a budget. How many miles are allowed?
Let m = miles. Set up 90 + 0.20m <= 250. Subtract 90: 0.20m <= 160. Divide: m <= 800 miles.
What words in a problem indicate which inequality symbol to use?
Words like at most, no more than, or maximum indicate <=. At least, no less than, or minimum indicate >=. Greater than means >. Less than means <.
Emma earns ,000/month and needs income at least 4x rent. What is maximum rent?
Let r = rent. Set up 6000 >= 4r. Divide both sides by 4: r <= 1500. Maximum rent is ,500/month.
Why does the solution to an inequality represent a range?
Because an inequality describes a constraint with multiple valid answers, not a single fixed value. Any value satisfying the inequality is a valid solution.
When do you flip the inequality sign?
Only when multiplying or dividing both sides by a negative number. Performing these operations reverses the inequality direction.