1Cademy - Solving a Rent Affordability Problem Using a Linear Inequality

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Linear Inequality

Example

Solving a Rent Affordability Problem Using a Linear Inequality

Apply the seven-step inequality strategy to a problem where income must be at least a given multiple of rent.

Problem: Emma's monthly income is $5,625. To qualify to rent an apartment, her monthly income must be at least three times the rent. What is the highest rent she will qualify for?

Read the problem.
Identify what to find: the highest rent Emma will qualify for.
Name the unknown: Let $r$ = the rent.
Translate into an inequality: "Emma's monthly income must be at least three times the rent" becomes

$5{,}625 \geq 3r$

Solve by dividing both sides by $3$ (a positive number, so the inequality direction is preserved):

$\frac{5{,}625}{3} \geq r$

$1{,}875 \geq r$

Recall that $a \geq x$ means the same as $x \leq a$ , so:

$r \leq 1{,}875$

Check: A maximum rent of $1,875 seems reasonable for an income of $5,625 since $3 \times 1{,}875 = 5{,}625$ .
Answer: The maximum rent Emma will qualify for is $1,875.

This example demonstrates how the phrase "at least" translates to a $\geq$ inequality, and how the Equivalence of Reversed Inequalities ( $a \geq x$ is the same as $x \leq a$ ) helps rewrite the result with the variable on the left side.

Updated 2026-04-21

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OpenStax Elementary Algebra

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