How Many Solutions? Practice

Question

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4 of 54 of 5 Items
Question
Solve for x
to determine if the equation has one, none, or infinite solutions.

6(2x+4)−24=12x

(1 point)
Responses

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 .

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

The equation has no solution.
The equation has no solution.
Remaining Attempts : 3

Answer 1

To solve the equation \(6(2x + 4) - 24 = 12x\), let’s first simplify the left side:

1. Distribute \(6\) into \((2x + 4)\): \[ 6 \cdot 2x + 6 \cdot 4 = 12x + 24 \] The equation becomes: \[ 12x + 24 - 24 = 12x \]

2. Simplify further: \[ 12x = 12x \]

This is an identity, meaning the equation is true for all values of \(x\). Thus, the equation has infinite solutions.

So the correct response is:

• The equation has infinite solutions.