Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

How many solutions does the equation have?

3x + 7 + 2x = 5x + 7

Sagot :

GinnyAnswer
To determine how many solutions the given equation
[tex]\[ 3x + 7 + 2x = 5x + 7 \][/tex]
has, let's proceed with the following steps:

1. Combine like terms on the left-hand side of the equation. Notice that [tex]\(3x\)[/tex] and [tex]\(2x\)[/tex] are like terms:
[tex]\[ 3x + 2x + 7 = 5x + 7 \][/tex]
Adding [tex]\(3x\)[/tex] and [tex]\(2x\)[/tex] gives:
[tex]\[ 5x + 7 = 5x + 7 \][/tex]

2. Simplify the equation by subtracting [tex]\(5x\)[/tex] from both sides:
[tex]\[ 5x + 7 - 5x = 5x + 7 - 5x \][/tex]
This simplifies to:
[tex]\[ 7 = 7 \][/tex]

3. This result is an identity. An identity means that both sides of the equation are equal for all values of [tex]\(x\)[/tex]. In this particular case, the equation does not depend on [tex]\(x\)[/tex] anymore and is just a true statement (7 equals 7).

Because the simplified equation is always true regardless of the value of [tex]\(x\)[/tex], it implies that there are infinitely many solutions to the original equation.

To summarize:
- The original equation simplifies to an identity [tex]\(7 = 7\)[/tex].
- This means that the equation holds true for any value of [tex]\(x\)[/tex].

Hence, there are infinitely many solutions.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.