Problem:
We are solving a compound inequality of the form:
$$ a < bx + c < d $$
Steps of solution:
Step 1: Isolate the term with 𝑥 by subtracting 𝑐 from all parts:
$$ a − c < bx < d − c $$
This step ensures that 𝑥 is on its own term.
Step 2: Divide all parts of the inequality by 𝑏 to isolate 𝑥:
$$ \frac{a - c}{b} < x < \frac{d - c}{b} $$
Now 𝑥 is isolated and the inequality is solved.
Final Step: Write the solution set in interval notation: The solution set is written as:
$$ (\frac{a - c}{b}, \frac{d - c}{b}) $$