he given equation is either linear or equivalent to a linear equation. Solve the equation. (If there is no solution, enter No solution. If all real numbers are solutions, enter REALS.) \[ \frac{4}{x}=\frac{5}{4 x}+1 \] Need Help? Read it Watch it

To solve the equation \( \frac{4}{x}=\frac{5}{4 x}+1 \), we first eliminate the fractions by multiplying through by \( 4x \), the common denominator. This gives us: \[ 4 \cdot 4 = 5 + 4x \] Simplifying this, we have: \[ 16 = 5 + 4x \] Subtracting 5 from both sides yields: \[ 11 = 4x \] Now, dividing both sides by 4 gives us: \[ x = \frac{11}{4} \] So the solution to the equation is \( x = \frac{11}{4} \). --- You can approach mathematical equations with a playful mindset! Think of \( x \) as a mystery character. In our case, after a bit of sleuthing, we discovered that our character is actually a very specific number: \( \frac{11}{4} \), just waiting to take the stage! Whenever you’re dealing with fractions and variables, it’s usually helpful to eliminate those pesky fractions first. Remember, multiplying both sides by the least common denominator can be your golden ticket! This way, you’re left with a linear equation that’s much easier to manage. Avoid the common pitfall of ignoring potential restrictions on \( x \)—like \( x \neq 0 \)!