Solve the following equation for x.

Express your answer in the simplest form.

2x-5=-3 2x+3)

Let's solve the equation \( 2x - 5 = -3(2x + 3) \).

### Step 1: Distribute the \(-3\) on the right side
\[
2x - 5 = -6x - 9
\]

### Step 2: Move all the \(x\) terms to one side and the constants to the other side
Add \(6x\) to both sides:
\[
2x + 6x - 5 = -9
\]
\[
8x - 5 = -9
\]

### Step 3: Add 5 to both sides to isolate the \(x\) term
\[
8x = -9 + 5
\]
\[
8x = -4
\]

### Step 4: Solve for \(x\) by dividing both sides by 8
\[
x = \frac{-4}{8}
\]
\[
x = -\frac{1}{2}
\]

So, the solution is \( x = -\frac{1}{2} \).

Would you like more details, or do you have any questions?

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Here are five related questions:

1. How would the solution change if the equation were \( 2x - 5 = -3(2x - 3) \)?
2. What is the value of \( x \) if the equation is \( 2x + 5 = -3(2x + 3) \)?
3. Can you solve \( 4x - 7 = -2(2x + 5) \) for \( x \)?
4. What happens if you substitute \( x = -\frac{1}{2} \) back into the original equation?
5. How would you solve \( 3x - 9 = -4(2x + 6) \)?

**Tip:** When dealing with negative signs in front of parentheses, be careful to distribute the sign correctly to avoid errors.

Learn how to solve the equation 2x - 5 = -3(2x + 3) with a detailed step-by-step solution. This problem covers key algebraic concepts including linear equations and the distributive property. Suitable for students in Grades 7-9.

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