To determine how many hours the plumber worked given the total bill of \[tex]$214, an initial charge of \$[/tex]130, and an hourly rate of \[tex]$56, we can model this problem with the equation:
\[130 + 56x = 214\]
Where \( x \) represents the number of hours worked.
### Step 1: Isolate the variable term
Operation: Subtraction
First, we need to isolate the term involving the variable \( x \) by eliminating the constant term on the left side of the equation.
To do this, we use the subtraction property of equality. We subtract 130 from both sides of the equation to remove the initial charge:
\[130 + 56x - 130 = 214 - 130\]
This simplifies to:
\[56x = 84\]
### Step 2: Solve for \( x \)
Next, to isolate \( x \), we need to divide both sides of the equation by 56 (which is the hourly rate). This makes use of the division property of equality:
\[ \frac{56x}{56} = \frac{84}{56} \]
Simplifying this:
\[ x = 1.5 \]
### Interpretation of the result
Therefore, the number of hours the plumber worked is \(1.5\) hours. This means she worked for an hour and a half.
So, the plumber worked a total of \(1.5\) hours to accumulate a total bill of \$[/tex]214, given her initial charge and hourly rate.
