Question

Solve the following equation for x Express your answer in the simplest form

7(6x - 2) = 7(6x - 2)


The equation has

A: no solution

B: Infinitely many solutions

C: one solution ____
Answer
Solve the following equation for x Express your answer in the simplest form

-4(6x-8)=24x+32

The equation has

A: no solution

B: Infinitely many solutions

C: one solution ____
Answered by GPT-4o mini
To solve the equation \( 7(6x - 2) = 7(6x - 2) \), we can first notice that both sides of the equation are identical.

This means that for any value of \( x \), the left side will always equal the right side. Thus, this equation is true for every value of \( x \).

Therefore, the equation has:

**B: Infinitely many solutions.**
Answered by GPT-4o mini
Let's solve the equation step by step:

Given:
\[
-4(6x - 8) = 24x + 32
\]

First, distribute \(-4\) on the left side:
\[
-24x + 32 = 24x + 32
\]

Next, to isolate \(x\), let's move all terms involving \(x\) to one side and the constant terms to the other side. Adding \(24x\) to both sides:
\[
32 = 24x + 24x + 32
\]
This simplifies to:
\[
32 = 48x + 32
\]

Now, subtract \(32\) from both sides:
\[
0 = 48x
\]

Dividing both sides by \(48\):
\[
x = 0
\]

So, the solution is \( x = 0 \).

Since we found a specific solution, the answer is:

**C: one solution \(\, x = 0\).**