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Solve for $s$ . $\newline$ $\frac{5}{8} - \frac{3}{8}s = 2 - s$ $\newline$ $s =$ __

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Solve equations with variables on both sides: fractional coefficients

Full solution

Q. Solve for

s

.

\newline

\frac{5}{8} - \frac{3}{8}s = 2 - s

\newline

s =

__

Move terms with s: First, we want to get all the terms with s on one side of the equation and the constant terms on the other side. To do this, we can add $\frac{3}{8}s$ to both sides of the equation to move the term with s from the left side to the right side. $\newline$ $\frac{5}{8} - \frac{3}{8}s + \frac{3}{8}s = 2 - s + \frac{3}{8}s$ $\newline$ $\frac{5}{8} = 2 - s + \frac{3}{8}s$
Combine terms with s: Now, we combine the terms with s on the right side of the equation. $\newline$ $2 - s + \frac{3}{8}s$ $\newline$ = $2 - \frac{8}{8}s + \frac{3}{8}s$ $\newline$ = $2 - \left(\frac{8}{8} - \frac{3}{8}\right)s$ $\newline$ = $2 - \frac{5}{8}s$
Rewrite equation: Next, we rewrite the equation after combining the terms with $s$ . $\frac{5}{8} = 2 - \left(\frac{5}{8}\right)s$ To isolate the variable term, we need to subtract $2$ from both sides of the equation. $\frac{5}{8} - 2 = - \left(\frac{5}{8}\right)s$
Subtract to isolate: We convert $2$ to a fraction with a denominator of $8$ to combine it with $\frac{5}{8}$ . $\newline$ $\frac{5}{8} - \frac{16}{8} = - \left(\frac{5}{8}\right)s$ $\newline$ $-\frac{11}{8} = - \left(\frac{5}{8}\right)s$
Convert to fractions: Now, we solve for $s$ by dividing both sides of the equation by $-\frac{5}{8}$ . $\newline$ $-\frac{11}{8} \div -\frac{5}{8} = s$ $\newline$ To divide by a fraction, we multiply by its reciprocal. $\newline$ $-\frac{11}{8} \times -\frac{8}{5} = s$
Solve for $s$ : We simplify the multiplication by canceling out the common factors. $-11 \times -1 = s$ $11 = s$

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