To determine the number of hours the plumber worked, given the total bill of \[tex]$214, the starting fee of \$[/tex]130, and the hourly rate of \[tex]$56, we can break down the problem step-by-step as follows:
### Step 1: Isolate the variable term
The given equation is:
\[
130 + 56x = 214
\]
To isolate the term containing \( x \) (the number of hours worked), we need to get rid of the starting fee of \$[/tex]130 on the left side of the equation by subtracting \$130 from both sides of the equation:
[tex]\[
130 + 56x - 130 = 214 - 130
\][/tex]
This simplifies to:
[tex]\[
56x = 84
\][/tex]
### Step 2: Solve for [tex]\( x \)[/tex]
Now, we need to solve for [tex]\( x \)[/tex] by isolating it on one side of the equation. Since [tex]\( 56x \)[/tex] means [tex]\( 56 \)[/tex] times [tex]\( x \)[/tex], we can isolate [tex]\( x \)[/tex] by dividing both sides of the equation by 56 to make the coefficient of [tex]\( x \)[/tex] equal to 1:
[tex]\[
\frac{56x}{56} = \frac{84}{56}
\][/tex]
This simplifies to:
[tex]\[
x = 1.5
\][/tex]
### Conclusion
Thus, the number of hours the plumber worked is 1.5 hours.
