3(4x + 8) = 4(3x + 6)

Answer 1

To solve the equation \(3(4x + 8) = 4(3x + 6)\), we can start by expanding both sides of the equation:

1. Expand the left side: \[ 3(4x + 8) = 3 \cdot 4x + 3 \cdot 8 = 12x + 24 \]

2. Expand the right side: \[ 4(3x + 6) = 4 \cdot 3x + 4 \cdot 6 = 12x + 24 \]

So the equation becomes: \[ 12x + 24 = 12x + 24 \]

Next, we can subtract \(12x\) from both sides: \[ 12x + 24 - 12x = 12x + 24 - 12x \] This simplifies to: \[ 24 = 24 \]

Since this is a true statement, it means that the equation holds for any value of \(x\). Therefore, the solution set is all real numbers, or: \[ \text{All } x \in \mathbb{R} \]

Answer 2

I dont understand

Answer 3

No problem! Let’s break it down step by step.

We started with the equation:

\[ 3(4x + 8) = 4(3x + 6) \]

Step 1: Distribute on both sides

First, we expand or distribute the numbers outside the parentheses on both sides of the equation.

Left Side:

• We distribute \(3\) to both \(4x\) and \(8\): \[ 3(4x) + 3(8) = 12x + 24 \]

Right Side:

• We distribute \(4\) to both \(3x\) and \(6\): \[ 4(3x) + 4(6) = 12x + 24 \]

Now our equation looks like this:

\[ 12x + 24 = 12x + 24 \]

Step 2: Simplify

Next, we try to simplify the equation by getting all terms involving \(x\) on one side.

Subtract \(12x\) from both sides of the equation:

\[ 12x + 24 - 12x = 12x + 24 - 12x \]

This simplifies to:

\[ 24 = 24 \]

Step 3: Interpretation

The statement \(24 = 24\) is always true and does not depend on the value of \(x\).

Conclusion

Since both sides of the equation are equal regardless of \(x\), it means any value of \(x\) will satisfy the equation. Thus, the solution is:

All real numbers (you can express this as \(x \in \mathbb{R}\)).

If you still have questions or would like me to explain a specific part further, feel free to ask!

Answer 4

Please give me an example of an equation that has one solution

Answer 5

Sure! One example of an equation that has exactly one solution is:

\[ 2x + 3 = 7 \]

Step-by-Step Solution

Let's solve this equation:

1. Start with the equation: \[ 2x + 3 = 7 \]

2. Subtract 3 from both sides to isolate the term with \(x\): \[ 2x + 3 - 3 = 7 - 3 \] This simplifies to: \[ 2x = 4 \]

3. Divide both sides by 2 to solve for \(x\): \[ \frac{2x}{2} = \frac{4}{2} \] This simplifies to: \[ x = 2 \]

Conclusion

The solution to the equation \(2x + 3 = 7\) is \(x = 2\).

This equation has exactly one solution: the value \(x = 2\). If you substitute \(2\) back into the original equation, you can verify that it holds true:

\[ 2(2) + 3 = 4 + 3 = 7 \]

Feel free to ask more questions or for further examples!