Solve -100/9k+(k-3)=155/9

$$\frac { - 100 } { 9 } k + ( k - 3 ) = \frac { 155 } { 9 }$$

Solve for k

$$k=-2$$

Steps for Solving Linear Equation

Fraction \frac{-100}{9} can be rewritten as -\frac{100}{9} by extracting the negative sign.

$$-\frac{100}{9}k+k-3=\frac{155}{9}$$

Combine -\frac{100}{9}k and k to get -\frac{91}{9}k.

$$-\frac{91}{9}k-3=\frac{155}{9}$$

Add 3 to both sides.

$$-\frac{91}{9}k=\frac{155}{9}+3$$

Convert 3 to fraction \frac{27}{9}.

$$-\frac{91}{9}k=\frac{155}{9}+\frac{27}{9}$$

Since \frac{155}{9} and \frac{27}{9} have the same denominator, add them by adding their numerators.

$$-\frac{91}{9}k=\frac{155+27}{9}$$

Add 155 and 27 to get 182.

$$-\frac{91}{9}k=\frac{182}{9}$$

Multiply both sides by -\frac{9}{91}, the reciprocal of -\frac{91}{9}.

$$k=\frac{182}{9}\left(-\frac{9}{91}\right)$$

Multiply \frac{182}{9} times -\frac{9}{91} by multiplying numerator times numerator and denominator times denominator.

$$k=\frac{182\left(-9\right)}{9\times 91}$$

Do the multiplications in the fraction \frac{182\left(-9\right)}{9\times 91}.

$$k=\frac{-1638}{819}$$

Divide -1638 by 819 to get -2.

$$k=-2$$