What value for a will result into a equation with infintely many solutions? **Question 6:**What value for \( a \) will result in an equation with infinitely many solutions?Given equation:\[ a(x + 5) = 3x + 15 \]**Detailed Explanation:**To find the value of \( a \) that results in infinitely many solutions, set the expressions equal by comparing the coefficients and constants once the equation is simplified.### Steps to Solve:1. **Distribute \( a \) in the expression:** \[ a(x + 5) = ax + 5a \]2. **Set the equations equal:** \[ ax + 5a = 3x + 15 \]3. **Compare coefficients and constants:** - Coefficient of \( x \): \( a = 3 \) - Constant term: \( 5a = 15 \)4. **Solve for \( a \) in the constant equation:** \[ 5a = 15 \implies a = \frac{15}{5} = 3 \]Since both conditions agree, \( a = 3 \) is the correct value for infinitely many solutions.

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Answered: What value for a will result in an…

What value for a will result in an equation with infintely many solutions? a(x + 5) = 3x + 15

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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