Question

Math 8B Unit 4 Study Guide
11. Which of the following equations has no solutions?
A. 4x + 1 = 4x + 2
B. 4x + 1 = 4x + 1
C. —4x + 1 = 4x + 2
D.
4x + 1=-4x+2

Answer 1

To determine which of the given equations has no solutions, we can analyze each one individually:

A. \( 4x + 1 = 4x + 2 \)

Subtracting \( 4x \) from both sides, we have:
\[ 1 = 2 \]
This statement is false, meaning this equation has no solutions.

B. \( 4x + 1 = 4x + 1 \)

Subtracting \( 4x \) from both sides, we have:
\[ 1 = 1 \]
This statement is always true, meaning this equation has infinitely many solutions.

C. \( -4x + 1 = 4x + 2 \)

Adding \( 4x \) to both sides, we have:
\[ 1 = 8x + 2 \]

Then, subtract \( 2 \) from both sides:
\[ -1 = 8x \]

Dividing both sides by \( 8 \):
\[ x = -\frac{1}{8} \]
This equation has one solution.

D. \( 4x + 1 = -4x + 2 \)

Adding \( 4x \) to both sides, we have:
\[ 8x + 1 = 2 \]

Then, subtract \( 1 \) from both sides:
\[ 8x = 1 \]

Dividing both sides by \( 8 \):
\[ x = \frac{1}{8} \]
This equation has one solution.

Thus, the equation that has no solutions is:

**A. \( 4x + 1 = 4x + 2 \)**.