Please show work and help me understand this multi-step equation.

The correct answer is a = 17/9.

Step-by-step explanation:

To begin this problem, we should use the distributive property on the left side of the equation to get rid of the parentheses.  This means that we can multiply each term inside the parentheses by the coefficient outside the parentheses.  This is modeled below:

3a - 2 = 3/4a + 2 1/4

Next, we should change the mixed number into an improper fraction so that it is easier to work with.

3a - 2 = 3/4a + 9/4

Now, we can multiply both sides of the equation by 4.  This is not a required step, but it will get rid of the fractions on the right side of the equation, so we only have to work in full numbers.

12a - 8 = 3a + 9

The next step is to subtract 3a from both sides and add 8 to both sides to separate the variable and constant terms.

12a - 3a - 8 + 8 = 3a - 3a + 9 + 8

9a = 17

Next, we can divide both sides by 9 to get our variable a alone on the left side of the equation.

a = 17/9

Therefore, the correct answer is a = 17/9.

Hi there!

One way to find the solution is to list out all of the possible combinations- which, in most cases, will take a long time.

Another more effective way to find the possible combinations is to multiply the amount of each component together and find the product of all of the amounts of items combined. 

In this case, you would multiply:

6 * 3 * 3 * 3 * 3
= 486. 

So, there'd be 486 combinations. 

Hope this helps!