Solve for x

Question

to determine if the equation has one, none, or infinite solutions.

6(2x+4)−24=12x

(1 point)
Responses

The equation has no solution.
The equation has no solution.

The equation has one solution: x=−20
.
The equation has one solution: x equals negative 20 .

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=0
.
The equation has one solution: x equals 0 .
Remaining Attempts : 3
Skip to navigation

page 12 of 13

Answer 1

Let's solve the equation step by step:

Given: \[ 6(2x + 4) - 24 = 12x \]

1. Distribute the 6 on the left side: \[ 6 \cdot 2x + 6 \cdot 4 - 24 = 12x \] \[ 12x + 24 - 24 = 12x \]

2. Simplify the left side: \[ 12x + 0 = 12x \] \[ 12x = 12x \]

This tells us that the left side and right side are equal for all values of \( x \). This is a true statement regardless of the value of \( x \).

Therefore, the equation has infinite solutions.

Conclusion: The correct response is: The equation has infinite solutions.