Determine the value of x in this equation. Share each step in the process.

2/5(x+15)=26

1 answer

To determine the value of \( x \) in the equation

\[ \frac{2}{5}(x + 15) = 26, \]

we can follow these steps:

Step 1: Eliminate the Fraction

To eliminate the fraction, we can multiply both sides of the equation by 5:

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

This simplifies to:

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

Step 2: Distribute the 2

Next, we distribute the 2 on the left side of the equation:

\[ 2x + 30 = 130. \]

Step 3: Isolate the Term with x

Now, we need to isolate the term with \( x \). We can do this by subtracting 30 from both sides of the equation:

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

This simplifies to:

\[ 2x = 100. \]

Step 4: Solve for x

Finally, we divide both sides of the equation by 2 to solve for \( x \):

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

This gives us:

\[ x = 50. \]

Conclusion

The value of \( x \) is

\[ \boxed{50}. \]