Solve -7/8k-2/7=7+2/5k

$$- \frac { 7 } { 8 } k - \frac { 2 } { 7 } = 7 + \frac { 2 } { 5 } k$$

Solve for k

$$k = -\frac{40}{7} = -5\frac{5}{7} \approx -5.714285714$$

Steps for Solving Linear Equation

Subtract \frac{2}{5}k from both sides.

$$-\frac{7}{8}k-\frac{2}{7}-\frac{2}{5}k=7$$

Combine -\frac{7}{8}k and -\frac{2}{5}k to get -\frac{51}{40}k.

$$-\frac{51}{40}k-\frac{2}{7}=7$$

Add \frac{2}{7} to both sides.

$$-\frac{51}{40}k=7+\frac{2}{7}$$

Convert 7 to fraction \frac{49}{7}.

$$-\frac{51}{40}k=\frac{49}{7}+\frac{2}{7}$$

Since \frac{49}{7} and \frac{2}{7} have the same denominator, add them by adding their numerators.

$$-\frac{51}{40}k=\frac{49+2}{7}$$

Add 49 and 2 to get 51.

$$-\frac{51}{40}k=\frac{51}{7}$$

Multiply both sides by -\frac{40}{51}, the reciprocal of -\frac{51}{40}.

$$k=\frac{51}{7}\left(-\frac{40}{51}\right)$$

Multiply \frac{51}{7} times -\frac{40}{51} by multiplying numerator times numerator and denominator times denominator.

$$k=\frac{51\left(-40\right)}{7\times 51}$$

Cancel out 51 in both numerator and denominator.

$$k=\frac{-40}{7}$$

Fraction \frac{-40}{7} can be rewritten as -\frac{40}{7} by extracting the negative sign.

$$k=-\frac{40}{7}$$