Question

Construct an equation that has k = 4 as its solution. Use k on both sides of the equation.

Answer 1

$\frac{3}{2}k - 7 = \frac{k}{4} - 2$

Since our fractions have two different denominators of 2 and 4 in this equation, we can get rid of the fractions by multiplying both sides of the equation by their common denominator, which is 4.

So we have $(4)(\frac{3}{2}k - 7) = (\frac{k}{4} - 2)(4)$.

Make sure you distribute the 4 through both

terms on both sides of the equation.

On the left, (4)(3/2k) is 6k and (4)(-7) is -28.

On the right, (4)(k/4) is k and (4)(-2) is -8.

So we have 6k - 28 = k - 8.

Now subtract k from both sides to get 5k - 28 = -8.

Now add 28 to both sides to get 5k = 20.

Finally, dividing both sides by 5, we find that k = 4.