Solve k+1/3+1=3k+1/2

$$\frac { k + 1 } { 3 } + 1 = \frac { 3 k + 1 } { 2 }$$

Solve for k

$$k=\frac{5}{7}\approx 0.714285714$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(k+1\right)+6=3\left(3k+1\right)$$

Use the distributive property to multiply 2 by k+1.

$$2k+2+6=3\left(3k+1\right)$$

Add 2 and 6 to get 8.

$$2k+8=3\left(3k+1\right)$$

Use the distributive property to multiply 3 by 3k+1.

$$2k+8=9k+3$$

Subtract 9k from both sides.

$$2k+8-9k=3$$

Combine 2k and -9k to get -7k.

$$-7k+8=3$$

Subtract 8 from both sides.

$$-7k=3-8$$

Subtract 8 from 3 to get -5.

$$-7k=-5$$

Divide both sides by -7.

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

Fraction \frac{-5}{-7} can be simplified to \frac{5}{7} by removing the negative sign from both the numerator and the denominator.

$$k=\frac{5}{7}$$