15. \( \frac{3}{5} x+22=28 \)

To solve the equation \( \frac{3}{5} x + 22 = 28 \), start by isolating \( \frac{3}{5} x \). Subtract 22 from both sides: \[ \frac{3}{5} x = 28 - 22 \] This simplifies to: \[ \frac{3}{5} x = 6 \] Next, to solve for \( x \), multiply both sides by the reciprocal of \( \frac{3}{5} \), which is \( \frac{5}{3} \): \[ x = 6 \times \frac{5}{3} \] Calculating that gives: \[ x = 10 \] So, the solution to the equation is \( x = 10 \). Next, if you're ever puzzled by fractions in equations, remember that fractions can be tricky but fun! Clearing fractions can sometimes make life easier; multiplying the entire equation by the denominator clears those pesky fractions right out of the way! Now, imagine you're facing something similar in real life; let’s say you're piecing together a recipe that has fractional measurements. A common mistake would be adding the fractions directly instead of first converting everything to a common denominator. Always keep an eye on your fractions, and remember, practice makes perfect!