Question

Which of the following equations does not have​ {all real​ numbers} as its solution​ set?
A. 7x=5x+2x     B. 2​(x+7​)=2x+14    C. three halves x=1.5x     D. 6x=5x

Answer 1

To determine which of the given equations does not have all real numbers as its solution set, we will solve each equation and analyze the solution:

A. \( 7x = 5x + 2x \)
Simplifying, we get:
\[ 7x = 7x \]
This is true for all \( x \).

B. \( 2(x + 7) = 2x + 14 \)
Expanding the left side:
\[ 2x + 14 = 2x + 14 \]
This is also true for all \( x \).

C. \( \frac{3}{2}x = 1.5x \)
Rewriting \( 1.5x \) as \( \frac{3}{2}x \):
\[ \frac{3}{2}x = \frac{3}{2}x \]
This holds true for all \( x \).

D. \( 6x = 5x \)
Subtracting \( 5x \) from both sides gives:
\[ 6x - 5x = 0 \]
\[ x = 0 \]
This has a specific solution: \( x = 0 \), not all real numbers.

Therefore, the equation that does not have all real numbers as its solution set is:

**D. \( 6x = 5x \)**