Questions: Solve and check the equation. 9x - (3x - 15) = 40 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is 3. (Type an integer or a simplified fraction.) B. The solution set is x x is a real number. C. The solution set is ∅.

Solution Steps

To solve the equation \(9x - (3x - 15) = 40\), we need to simplify and solve for \(x\). First, distribute and combine like terms, then isolate \(x\) on one side of the equation. Finally, check the solution by substituting it back into the original equation.

We start with the equation: \[ 9x - (3x - 15) = 40 \] Distributing the negative sign gives: \[ 9x - 3x + 15 = 40 \] Combining like terms results in: \[ 6x + 15 = 40 \]

Next, we isolate \(x\) by subtracting 15 from both sides: \[ 6x = 40 - 15 \] This simplifies to: \[ 6x = 25 \] Now, we divide both sides by 6: \[ x = \frac{25}{6} \]

To verify our solution, we substitute \(x = \frac{25}{6}\) back into the original equation: \[ 9\left(\frac{25}{6}\right) - \left(3\left(\frac{25}{6}\right) - 15\right) = 40 \] Calculating the left side: \[ \frac{225}{6} - \left(\frac{75}{6} - 15\right) = 40 \] Converting 15 to sixths gives: \[ \frac{225}{6} - \left(\frac{75}{6} - \frac{90}{6}\right) = 40 \] This simplifies to: \[ \frac{225}{6} - \left(-\frac{15}{6}\right) = 40 \] Thus: \[ \frac{225 + 15}{6} = 40 \quad \Rightarrow \quad \frac{240}{6} = 40 \] Since both sides are equal, the solution is confirmed.

Final Answer