Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Solve and check the equation:

[tex]\[ 3x + 7 = 2x + 15 \][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is [tex]\(\{ \ \square \ \}\)[/tex].
(Type an integer or a simplified fraction.)

B. The solution set is [tex]\(\{ x \mid x \text{ is a real number} \}\)[/tex].

C. The solution set is [tex]\(\varnothing\)[/tex].

Sagot :

GinnyAnswer
Alright! Let's go through the process of solving the given equation step-by-step:

The equation given to us is:

[tex]\[ 3x + 7 = 2x + 15 \][/tex]

Our goal is to solve for the variable [tex]\( x \)[/tex]. We will start by isolating [tex]\( x \)[/tex].

### Step 1: Move terms involving [tex]\( x \)[/tex] to one side of the equation
First, we should eliminate [tex]\( 2x \)[/tex] from the right side by subtracting [tex]\( 2x \)[/tex] from both sides:

[tex]\[ 3x + 7 - 2x = 2x + 15 - 2x \][/tex]

Which simplifies to:

[tex]\[ x + 7 = 15 \][/tex]

### Step 2: Simplify the equation
Now, we want to isolate [tex]\( x \)[/tex] further by getting rid of the constant term on the left side. We do this by subtracting 7 from both sides:

[tex]\[ x + 7 - 7 = 15 - 7 \][/tex]

Which simplifies to:

[tex]\[ x = 8 \][/tex]

### Step 3: Check the solution
We need to verify that [tex]\( x = 8 \)[/tex] satisfies the original equation. Substitute [tex]\( x = 8 \)[/tex] back into the original equation:

[tex]\[ 3(8) + 7 = 2(8) + 15 \][/tex]

Calculate each side:

[tex]\[ 24 + 7 = 16 + 15 \][/tex]

[tex]\[ 31 = 31 \][/tex]

Since both sides of the equation are equal when [tex]\( x = 8 \)[/tex], our solution is verified.

Hence, the solution set for the equation is:

A. [tex]\(\{ 8 \}\)[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.