Which represents the solution set of $5(x+5)<85$?
A. $x<12$
B. $x>12$
C. $x<16$
D. $x>16$
Answer (2)
The solution to the inequality 5 ( x + 5 ) < 85 is x < 12 . Therefore, the correct option is A. x < 12 .
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Distribute the constant: 5 ( x + 5 ) < 85 becomes 5 x + 25 < 85 .
Subtract 25 from both sides: 5 x < 60 .
Divide by 5: x < 12 .
The solution set is x < 12 .
Explanation
Understanding the Inequality We are given the inequality 5 ( x + 5 ) < 85 . Our goal is to isolate x to find the solution set.
Distributing the Constant First, distribute the 5 on the left side of the inequality:
5 ( x + 5 ) < 85
5 x + 25 < 85
Isolating the x Term Next, subtract 25 from both sides of the inequality to isolate the term with x :
5 x + 25 − 25 < 85 − 25
5 x < 60
Solving for x Now, divide both sides of the inequality by 5 to solve for x :
5 5 x < 5 60
x < 12
Final Answer Therefore, the solution set for the inequality 5 ( x + 5 ) < 85 is x < 12 .
Examples
Understanding inequalities is crucial in many real-world scenarios. For instance, when budgeting, you might want to ensure that your expenses ( x ) plus a fixed cost (e.g., $5) multiplied by a certain factor (e.g., $5) remains below a certain limit (e.g., $85). The inequality 5 ( x + 5 ) < 85 helps you determine the maximum amount you can spend while staying within your budget. Similarly, in manufacturing, you might use inequalities to ensure that the dimensions of a product fall within acceptable tolerances.
