Solve 1/2*k/a*(-a)=3/2

$$\frac { 1 } { 2 } \times \frac { k } { a } \cdot ( - a ) = \frac { 3 } { 2 }$$

Solve for a

$$a\neq 0$$

$$k=-3$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2a, the least common multiple of 2,a.

$$\frac{1}{2}\times 2k\left(-a\right)=3a$$

Multiply \frac{1}{2} and 2 to get 1.

$$k\left(-a\right)=3a$$

Subtract 3a from both sides.

$$k\left(-a\right)-3a=0$$

Reorder the terms.

$$-ak-3a=0$$

Combine all terms containing a.

$$\left(-k-3\right)a=0$$

Divide 0 by -3-k.

$$a=0$$

Variable a cannot be equal to 0.

$$a\in \emptyset$$

Solve for k

$$k=-3$$

$$a\neq 0$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}\times 2k\left(-a\right)=3a$$

Multiply \frac{1}{2} and 2 to get 1.

$$k\left(-a\right)=3a$$

Reorder the terms.

$$-ak=3a$$

The equation is in standard form.

$$\left(-a\right)k=3a$$

Divide both sides by -a.

$$\frac{\left(-a\right)k}{-a}=\frac{3a}{-a}$$

Dividing by -a undoes the multiplication by -a.

$$k=\frac{3a}{-a}$$

Divide 3a by -a.

$$k=-3$$