Solve for a.

Steps to Solve

1. Write the equation clearly

The equation is given by: $$ -\frac{1}{3}a = -\frac{3}{4}a - 2 + \frac{5}{2}a $$

2. Combine like terms on the right side

Let's simplify the right side of the equation:

• Combine $-\frac{3}{4}a$ and $\frac{5}{2}a$.

Convert $\frac{5}{2}$ into a fraction with a common denominator of 4: $$ \frac{5}{2} = \frac{10}{4} $$

Now, we can combine: $$ -\frac{3}{4}a + \frac{10}{4}a = \frac{7}{4}a $$

So, the equation now looks like: $$ -\frac{1}{3}a = \frac{7}{4}a - 2 $$

3. Move the terms involving 'a' to one side

Add $\frac{1}{3}a$ to both sides of the equation: $$ 0 = \frac{7}{4}a + \frac{1}{3}a - 2 $$

4. Find a common denominator for the 'a' terms

The common denominator for 4 and 3 is 12. Convert the terms: $$ \frac{7}{4}a = \frac{21}{12}a $$ $$ \frac{1}{3}a = \frac{4}{12}a $$

Combine these: $$ 0 = \left(\frac{21}{12}a + \frac{4}{12}a\right) - 2 $$ $$ 0 = \frac{25}{12}a - 2 $$

5. Isolate 'a'

Add 2 to both sides: $$ 2 = \frac{25}{12}a $$

Now, multiply both sides by the reciprocal of $\frac{25}{12}$, which is $\frac{12}{25}$: $$ a = 2 \times \frac{12}{25} $$

6. Calculate the value of 'a'

Compute: $$ a = \frac{24}{25} $$