Let's solve this problem step-by-step as if we are working it out manually.
### Step 1: Setting up the Equation
You correctly identified the equation:
[tex]\[ 130 + 56x = 214 \][/tex]
where [tex]\( x \)[/tex] represents the number of hours the plumber worked.
### Step 2: Solve for Variable 'x'
First, we need to isolate the term containing the variable [tex]\( x \)[/tex]. To do this, we'll subtract 130 (the initial charge) from both sides of the equation.
[tex]\[
130 + 56x - 130 = 214 - 130
\][/tex]
Simplifying this, we get:
[tex]\[
56x = 84
\][/tex]
### Step 3: Divide to Isolate 'x'
Next, to solve for [tex]\( x \)[/tex], we need to divide both sides of the equation by the coefficient of [tex]\( x \)[/tex], which is 56.
[tex]\[
\frac{56x}{56} = \frac{84}{56}
\][/tex]
This simplifies to:
[tex]\[
x = 1.5
\][/tex]
### Interpretation
The variable [tex]\( x \)[/tex] represents the number of hours the plumber worked. So, from our calculations, [tex]\( x = 1.5 \)[/tex], meaning the plumber worked for 1.5 hours.
### Conclusion
The plumber worked for 1.5 hours if the total bill is \$214.
