Solve -2+k/5=2-(-2)/3

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

Solve for k

$$k = \frac{26}{3} = 8\frac{2}{3} \approx 8.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3\left(-2+k\right)=5\left(2-\left(-2\right)\right)$$

Use the distributive property to multiply 3 by -2+k.

$$-6+3k=5\left(2-\left(-2\right)\right)$$

The opposite of -2 is 2.

$$-6+3k=5\left(2+2\right)$$

Add 2 and 2 to get 4.

$$-6+3k=5\times 4$$

Multiply 5 and 4 to get 20.

$$-6+3k=20$$

Add 6 to both sides.

$$3k=20+6$$

Add 20 and 6 to get 26.

$$3k=26$$

Divide both sides by 3.

$$k=\frac{26}{3}$$