Solve the equation. Select the solution 1/2(4x+6)-11=5x+7




Let's solve the given equation step by step:

\[
\frac{1}{2}(4x + 6) - 11 = 5x + 7
\]

### Step 1: Distribute the \(\frac{1}{2}\) on the left-hand side
\[
\frac{1}{2}(4x) + \frac{1}{2}(6) - 11 = 5x + 7
\]
This simplifies to:
\[
2x + 3 - 11 = 5x + 7
\]

### Step 2: Combine like terms on the left-hand side
\[
2x - 8 = 5x + 7
\]

### Step 3: Move all terms involving \(x\) to one side and constant terms to the other side
\[
2x - 5x = 7 + 8
\]
This simplifies to:
\[
-3x = 15
\]

### Step 4: Solve for \(x\)
\[
x = \frac{15}{-3} = -5
\]

Thus, the solution is:
\[
x = -5
\]

Would you like more details on any step? 

Here are 5 related questions:
1. How do you solve linear equations with fractions?
2. What are the steps to isolate variables in an equation?
3. How do you verify the solution to a linear equation?
4. Can linear equations have more than one solution?
5. What happens if the variable cancels out in a linear equation?

**Tip:** Always check your solution by plugging it back into the original equation to verify its correctness.

Solve the equation. Select the solution 1/2(4x+6)-11=5x+7

Learn how to solve the linear equation 1/2(4x + 6) - 11 = 5x + 7 with step-by-step instructions. This algebraic problem covers key concepts like the distributive property and solving for x. Suitable for students in Grades 8-10.

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