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

4, left parenthesis, minus, 2, x, minus, 1, right parenthesis, equals, minus, 12, x, plus, 9

4(−2*x*−1)=

−12*x*+9

Let's solve the equation \( 4(-2x - 1) = -12x + 9 \) step by step:

### Step 1: Distribute on the left-hand side
Distribute the \( 4 \) across \( (-2x - 1) \):

\[
4(-2x) + 4(-1) = -8x - 4
\]

So the equation becomes:

\[
-8x - 4 = -12x + 9
\]

### Step 2: Move the variable terms to one side
Add \( 12x \) to both sides to move all \( x \)-terms to one side:

\[
-8x + 12x - 4 = 9
\]

This simplifies to:

\[
4x - 4 = 9
\]

### Step 3: Move the constant term to the other side
Add \( 4 \) to both sides:

\[
4x = 9 + 4
\]

\[
4x = 13
\]

### Step 4: Solve for \( x \)
Divide both sides by \( 4 \):

\[
x = \frac{13}{4}
\]

### Final Answer:
\[
x = \frac{13}{4}
\]

This is the simplest form of the solution.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How would the solution change if the constant term on the right side was negative, such as \( -9 \)?
2. What if the coefficient of \( x \) on the right-hand side was different, like \( -10x + 9 \)?
3. Can you solve a similar equation where both sides contain decimals?
4. How do you solve an equation where the left side involves fractions?
5. What happens if you have more than one distributive term on each side of the equation?

**Tip**: Always simplify both sides by distributing before combining like terms and moving variables or constants!

Solve the following equation for x: 4(−2x − 1) = −12x + 9. Express your answer in the simplest form.

Learn how to solve the linear equation 4(-2x - 1) = -12x + 9 with a step-by-step solution. This problem demonstrates the use of the distributive property and variable isolation techniques. Perfect for students in Grades 8-10.

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