Solve the equation. Then determine whether the equation is an identity, a condif equation. \[ 9 x+7=5 x+7 \] What is the solution? Select the correct choice below and, if necessary fill in the a

To solve the equation and determine its nature, let's follow these steps: **Given Equation:** \[ 9x + 7 = 5x + 7 \] **Step 1: Solve for \( x \)** 1. **Subtract \( 5x \) from both sides** to get the variable terms on one side: \[ 9x + 7 - 5x = 5x + 7 - 5x \\ 4x + 7 = 7 \] 2. **Subtract 7 from both sides** to isolate the term with \( x \): \[ 4x + 7 - 7 = 7 - 7 \\ 4x = 0 \] 3. **Divide both sides by 4** to solve for \( x \): \[ x = 0 \] **Solution:** \[ x = 0 \] **Step 2: Determine the Nature of the Equation** - **Identity:** An equation that is true for all real numbers \( x \). - **Conditional Equation:** An equation that is true for specific values of \( x \). - **Contradiction:** An equation that has no solution. In this case, the equation \( 9x + 7 = 5x + 7 \) simplifies to \( x = 0 \), which means **only \( x = 0 \) satisfies the equation**. **Conclusion:** - The equation has a **single solution** (\( x = 0 \)). - Therefore, it is a **conditional equation** because it is true **only for \( x = 0 \)**. **Final Answer:** - **Solution:** \( x = 0 \) - **Type of Equation:** Conditional equation