Sure, let's solve the equation step-by-step. The given equation is:
[tex]\[ 10\left( \frac{3a}{5} - 4 = \frac{3a}{2} - \frac{a}{2} \right) \][/tex]
First, let’s simplify both sides of the equation inside the parentheses.
### Left Side:
[tex]\[ \frac{3a}{5} - 4 \][/tex]
### Right Side:
[tex]\[ \frac{3a}{2} - \frac{a}{2} \][/tex]
[tex]\[ \frac{3a - a}{2} \][/tex]
[tex]\[ \frac{2a}{2} \][/tex]
[tex]\[ a \][/tex]
Now, the equation inside the parentheses becomes:
[tex]\[ \frac{3a}{5} - 4 = a \][/tex]
Next, let's solve for [tex]\( a \)[/tex].
### Step 1: Isolate variable terms on one side
First, we can move the term involving [tex]\( a \)[/tex] on the left side (i.e., [tex]\(\frac{3a}{5}\)[/tex]) to the right side by subtracting it from both sides:
[tex]\[ -4 = a - \frac{3a}{5} \][/tex]
### Step 2: Combine like terms
Convert [tex]\( a \)[/tex] into a fraction with a common denominator to combine like terms:
[tex]\[ a = \frac{5a}{5} \][/tex]
Now, the equation is:
[tex]\[ -4 = \frac{5a}{5} - \frac{3a}{5} \][/tex]
Combine the fractions:
[tex]\[ -4 = \frac{5a - 3a}{5} \][/tex]
[tex]\[ -4 = \frac{2a}{5} \][/tex]
### Step 3: Solve for [tex]\( a \)[/tex]
To isolate [tex]\( a \)[/tex], multiply both sides of the equation by 5:
[tex]\[ -4 \times 5 = 2a \][/tex]
[tex]\[ -20 = 2a \][/tex]
Divide both sides by 2:
[tex]\[ -20 / 2 = a \][/tex]
[tex]\[ a = -10 \][/tex]
So, the value of [tex]\( a \)[/tex] that satisfies the given equation is [tex]\( -10 \)[/tex].
### Summary:
After simplifying and solving the equation step-by-step, we find:
[tex]\[ a = -10 \][/tex]
- The left side simplification leads to: [tex]\(\frac{3a}{5} - 4\)[/tex].
- The right side simplification leads to: [tex]\(a\)[/tex].
- And finally, the solution to the equation is [tex]\( a = -10 \)[/tex].
