Solving Linear Equations II

Problem 253: Solve for $k$ in the following equation:

$\frac{-6}{2}k + \frac{9}{8} = -9 - \frac{-3}{8}k$

Solution: First, we will simplify the fractions that can be simplified.

$\frac{-6}{2}k + \frac{9}{8} = -9 - \frac{-3}{8}k \implies -3k + \frac{9}{8} = -9 -+\frac{3}{8}k$

Clear the denominator by multiplying by the least common multiple, 8.

$8\left(-3k + \frac{9}{8} = -9 -+\frac{3}{8}k \right) \implies -24k + 9 = -72 + 3k$

Simplify by combining like terms.

$-24k + 9 = -72 + 3k \implies -24k - 3k = -72 - 9 \implies -27k = - 81$

Solve for $k$ .

$-27k = - 81 \implies k = \frac{81}{27}=3$

That is,

$k = 3$ .