Solve (2k+1)3/4+(3+k)5+1-2k=0

$$( 2 k + 1 ) \frac { 3 } { 4 } + ( 3 + k ) 5 + 1 - 2 k = 0$$

Solve for k

$$k = -\frac{67}{18} = -3\frac{13}{18} \approx -3.722222222$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2k+1 by \frac{3}{4}.

$$2k\times \frac{3}{4}+\frac{3}{4}+\left(3+k\right)\times 5+1-2k=0$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{2\times 3}{4}k+\frac{3}{4}+\left(3+k\right)\times 5+1-2k=0$$

Multiply 2 and 3 to get 6.

$$\frac{6}{4}k+\frac{3}{4}+\left(3+k\right)\times 5+1-2k=0$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}k+\frac{3}{4}+\left(3+k\right)\times 5+1-2k=0$$

Use the distributive property to multiply 3+k by 5.

$$\frac{3}{2}k+\frac{3}{4}+15+5k+1-2k=0$$

Convert 15 to fraction \frac{60}{4}.

$$\frac{3}{2}k+\frac{3}{4}+\frac{60}{4}+5k+1-2k=0$$

Since \frac{3}{4} and \frac{60}{4} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}k+\frac{3+60}{4}+5k+1-2k=0$$

Add 3 and 60 to get 63.

$$\frac{3}{2}k+\frac{63}{4}+5k+1-2k=0$$

Combine \frac{3}{2}k and 5k to get \frac{13}{2}k.

$$\frac{13}{2}k+\frac{63}{4}+1-2k=0$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{13}{2}k+\frac{63}{4}+\frac{4}{4}-2k=0$$

Since \frac{63}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{13}{2}k+\frac{63+4}{4}-2k=0$$

Add 63 and 4 to get 67.

$$\frac{13}{2}k+\frac{67}{4}-2k=0$$

Combine \frac{13}{2}k and -2k to get \frac{9}{2}k.

$$\frac{9}{2}k+\frac{67}{4}=0$$

Subtract \frac{67}{4} from both sides. Anything subtracted from zero gives its negation.

$$\frac{9}{2}k=-\frac{67}{4}$$

Multiply both sides by \frac{2}{9}, the reciprocal of \frac{9}{2}.

$$k=-\frac{67}{4}\times \frac{2}{9}$$

Multiply -\frac{67}{4} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$k=\frac{-67\times 2}{4\times 9}$$

Do the multiplications in the fraction \frac{-67\times 2}{4\times 9}.

$$k=\frac{-134}{36}$$

Reduce the fraction \frac{-134}{36} to lowest terms by extracting and canceling out 2.

$$k=-\frac{67}{18}$$