Let's solve the equation step-by-step:
Given the equation:
[tex]\[ \frac{1}{5} x - 4 = 3(x - 5) \][/tex]
1. Distribute the 3 on the right-hand side:
[tex]\[ \frac{1}{5} x - 4 = 3x - 15 \][/tex]
2. Isolate the \( x \) terms on one side and the constants on the other side:
[tex]\[ \frac{1}{5} x - 3x = -15 + 4 \][/tex]
3. Combine the constants on the right-hand side:
[tex]\[ \frac{1}{5} x - 3x = -11 \][/tex]
4. To combine the \( x \) terms, we need to express \(\frac{1}{5} x\) in a form that can be easily combined with \(3x\):
[tex]\[ \frac{1}{5} x = \frac{x}{5} \][/tex]
So we rewrite the equation:
[tex]\[ \frac{x}{5} - 3x = -11 \][/tex]
5. Clear the fraction by multiplying every term by 5:
[tex]\[ x - 15x = -55 \][/tex]
6. Combine like terms:
[tex]\[ -14x = -55 \][/tex]
7. Solve for \( x \) by dividing both sides by -14:
[tex]\[ x = \frac{-55}{-14} \][/tex]
[tex]\[ x = \frac{55}{14} \][/tex]
So the solution to the equation is:
[tex]\[ x = \frac{55}{14} \approx 3.9285714285714284 \][/tex]
