Solve k-2/2=4-3k/3-2-k/5

$$\frac { k - 2 } { 2 } = \frac { 4 - 3 k } { 3 } - \frac { 2 - k } { 5 }$$

Solve for k

$$k = \frac{58}{39} = 1\frac{19}{39} \approx 1.487179487$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 2,3,5.

$$15\left(k-2\right)=10\left(4-3k\right)-6\left(2-k\right)$$

Use the distributive property to multiply 15 by k-2.

$$15k-30=10\left(4-3k\right)-6\left(2-k\right)$$

Use the distributive property to multiply 10 by 4-3k.

$$15k-30=40-30k-6\left(2-k\right)$$

Use the distributive property to multiply -6 by 2-k.

$$15k-30=40-30k-12+6k$$

Subtract 12 from 40 to get 28.

$$15k-30=28-30k+6k$$

Combine -30k and 6k to get -24k.

$$15k-30=28-24k$$

Add 24k to both sides.

$$15k-30+24k=28$$

Combine 15k and 24k to get 39k.

$$39k-30=28$$

Add 30 to both sides.

$$39k=28+30$$

Add 28 and 30 to get 58.

$$39k=58$$

Divide both sides by 39.

$$k=\frac{58}{39}$$