Question

Solve the equation.
3 left parenthesis 5 x minus 2 right parenthesis plus 8 left parenthesis negative 5 plus 2 x right parenthesis equals 6 left parenthesis 5 x minus 5 right parenthesis minus 6
Question content area bottom
Part 1
A.negative 82
negative 82
B.10
10
C.
All real numbers
D.
0

Answer 1

Let's solve the equation step-by-step:

1. **Start with the given equation:**
\[
3(5x - 2) + 8(-5 + 2x) = 6(5x - 5) - 6
\]

2. **Distribute on both sides:**

**Left side:**
\[
3(5x) - 3(2) + 8(-5) + 8(2x) = 15x - 6 - 40 + 16x
\]
Combine like terms:
\[
15x + 16x - 6 - 40 = 31x - 46
\]

**Right side:**
\[
6(5x) - 6(5) - 6 = 30x - 30 - 6
\]
Combine like terms:
\[
30x - 36
\]

3. **Now we have a simplified equation:**
\[
31x - 46 = 30x - 36
\]

4. **Subtract \(30x\) from both sides:**
\[
31x - 30x - 46 = -36
\]
Simplifying gives:
\[
x - 46 = -36
\]

5. **Add \(46\) to both sides:**
\[
x = 10
\]

Thus, the solution to the equation is:
\[
x = 10
\]

**The answer is B. 10.**