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Question
Solve for x:

x(8 + 2) + 3 = 2(5 + x) + 5(x + 1) − 6
Responses
A −4
B −2
C 2
D 4

Answer 1

To solve for \( x \) in the equation

\[
x(8 + 2) + 3 = 2(5 + x) + 5(x + 1) - 6,
\]

first, simplify both sides of the equation.

1. Simplify the left side:
\[
x(8 + 2) + 3 = x(10) + 3 = 10x + 3.
\]

2. Simplify the right side:
- Start with distributing the terms:
\[
2(5 + x) = 10 + 2x,
\]
and
\[
5(x + 1) = 5x + 5.
\]
- Combine these with \(-6\):
\[
10 + 2x + 5x + 5 - 6 = 10 + 5 - 6 + 2x + 5x = 9 + 7x.
\]

Now rewrite the equation with the simplified sides:

\[
10x + 3 = 9 + 7x.
\]

3. To solve for \( x \), first subtract \( 7x \) from both sides:

\[
10x - 7x + 3 = 9 \implies 3x + 3 = 9.
\]

4. Next, subtract 3 from both sides:

\[
3x = 6.
\]

5. Finally, divide both sides by 3:

\[
x = 2.
\]

Thus, the solution for \( x \) is

\[
\boxed{2}.
\]