Determine the value of x in this equation. You can choose the method you use to solve, but you must list ALL steps and the solution. 2/5(x+15)=26

Answer 1

To solve the equation \( \frac{2}{5}(x + 15) = 26 \), we will follow the steps outlined below:

Step 1: Eliminate the Fraction

To eliminate the fraction \(\frac{2}{5}\), multiply both sides of the equation by \(5\):

\[ 5 \cdot \left( \frac{2}{5}(x + 15) \right) = 5 \cdot 26 \]

This simplifies to:

\[ 2(x + 15) = 130 \]

Step 2: Distribute the 2

Next, distribute \(2\) on the left side:

\[ 2x + 30 = 130 \]

Step 3: Isolate the Variable Term

Now, we will isolate the term containing \(x\) by subtracting \(30\) from both sides:

\[ 2x + 30 - 30 = 130 - 30 \]

This simplifies to:

\[ 2x = 100 \]

Step 4: Solve for \(x\)

Now, divide both sides by \(2\) to solve for \(x\):

\[ x = \frac{100}{2} \]

This simplifies to:

\[ x = 50 \]

Conclusion

The value of \(x\) is

\[ \boxed{50} \]