To solve the equation \( \frac{5}{8} - \frac{3}{8}s = 2 - s \), follow these steps:
-
Start by isolating the terms with \( s \) on one side. You can add \( s \) to both sides and add \( \frac{3}{8}s \) to both sides: \[ \frac{5}{8} = 2 - s + \frac{3}{8}s \]
-
Rewrite the right side by combining the \( s \) terms: \[ \frac{5}{8} = 2 + \left(-1 + \frac{3}{8}\right)s \] To combine \( -1 \) and \( \frac{3}{8} \), convert \( -1 \) into eighths: \[ -1 = -\frac{8}{8} \] Thus, \[ -\frac{8}{8} + \frac{3}{8} = -\frac{5}{8} \] So we can rewrite the equation as: \[ \frac{5}{8} = 2 - \frac{5}{8}s \]
-
Now subtract \( 2 \) from both sides to keep the equation balanced: \[ \frac{5}{8} - 2 = -\frac{5}{8}s \] Convert \( 2 \) into eighths: \[ 2 = \frac{16}{8} \] Thus: \[ \frac{5}{8} - \frac{16}{8} = -\frac{5}{8}s \] This simplifies to: \[ -\frac{11}{8} = -\frac{5}{8}s \]
-
Now, to solve for \( s \), multiply through by -1: \[ \frac{11}{8} = \frac{5}{8}s \]
-
To isolate \( s \), multiply both sides by \( \frac{8}{5} \): \[ s = \frac{11}{8} \cdot \frac{8}{5} = \frac{11}{5} \]
Thus, the solution for \( s \) is: \[ s = \frac{11}{5} \]
1 answer