Let's solve the given equation step by step.
First, we start with the given equation:
[tex]\[ \frac{3}{5}(x - 10) = 18 - 4x - 1 \][/tex]
### Step 1: Distribute the \(\frac{3}{5}\) across the terms inside the parentheses
Distributing \(\frac{3}{5}\):
[tex]\[ \frac{3}{5} \cdot x - \frac{3}{5} \cdot 10 \][/tex]
This simplifies to:
[tex]\[ \frac{3}{5} x - 6 \][/tex]
So, the equation now looks like:
[tex]\[ \frac{3}{5} x - 6 = 18 - 4x - 1 \][/tex]
### Step 2: Combine like terms
On the right-hand side, combine 18 and -1:
[tex]\[ 18 - 1 = 17 \][/tex]
So, the equation becomes:
[tex]\[ \frac{3}{5} x - 6 = 17 - 4x \][/tex]
### Step 3: Move all the \(x\)-terms to one side and the constants to the other side
Add \(4x\) to both sides to move the \(x\)-terms to the left:
[tex]\[ \frac{3}{5} x + 4x - 6 = 17 \][/tex]
Convert \(4x\) to a fraction with denominator 5 for simplicity:
[tex]\[ \frac{3}{5} x + \frac{20}{5} x - 6 = 17 \][/tex]
[tex]\[ \frac{23}{5} x - 6 = 17 \][/tex]
Next, add 6 to both sides to isolate the term with \(x\):
[tex]\[ \frac{23}{5} x = 23 \][/tex]
### Step 4: Solve for \(x\)
Multiply both sides by \(\frac{5}{23}\) to solve for \(x\):
[tex]\[ x = 23 \cdot \frac{5}{23} \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution to the equation is:
[tex]\[ \boxed{x = 5} \][/tex]
