Question

ARENNER
Math 8B Unit 4 Study Guide
13. Solve for x to determine if the equation has one, none, or infinite solutions
9x=2（8x-3） -7x
A. The equation has one solution: x = -6.
B. The equation has infinite solutions.
C. The equation has no solutions.
D. The equation has one solution: x = 6.
11111

Answer 1

To solve the equation \(9x = 2(8x - 3) - 7x\), let's start by simplifying the equation step by step.

1. Distribute on the right side:
\[
9x = 2 \cdot 8x - 2 \cdot 3 - 7x
\]
\[
9x = 16x - 6 - 7x
\]

2. Combine like terms on the right side:
\[
9x = 16x - 7x - 6
\]
\[
9x = 9x - 6
\]

3. Next, let's isolate the variable \(x\). Subtract \(9x\) from both sides:
\[
9x - 9x = 9x - 6 - 9x
\]
\[
0 = -6
\]

This statement \(0 = -6\) is a contradiction, meaning there are no values of \(x\) that will satisfy the equation.

Thus, the answer is:
**C. The equation has no solutions.**