To solve the equation [tex]\(3x + 17 + 5x = 7x + 10\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Combine like terms on both sides of the equation:
[tex]\[
3x + 5x + 17 = 7x + 10
\][/tex]
Simplify the terms:
[tex]\[
8x + 17 = 7x + 10
\][/tex]
2. Isolate the term with [tex]\(x\)[/tex] on one side of the equation. To do this, subtract [tex]\(7x\)[/tex] from both sides:
[tex]\[
8x - 7x + 17 = 7x - 7x + 10
\][/tex]
Simplify the terms:
[tex]\[
x + 17 = 10
\][/tex]
3. Isolate [tex]\(x\)[/tex] by getting rid of the constant on the left side. Subtract 17 from both sides:
[tex]\[
x + 17 - 17 = 10 - 17
\][/tex]
Simplify the terms:
[tex]\[
x = -7
\][/tex]
So, the solution to the equation [tex]\(3x + 17 + 5x = 7x + 10\)[/tex] is [tex]\(x = -7\)[/tex].
Looking at the provided options:
A. [tex]\(x = 27\)[/tex]
B. [tex]\(x = -7\)[/tex]
C. [tex]\(x = \frac{27}{15}\)[/tex]
D. [tex]\(x = -\frac{7}{15}\)[/tex]
The correct answer is:
B. [tex]\(x = -7\)[/tex]
