To solve the equation [tex]\( 130 + 56x = 214 \)[/tex], we need to isolate the variable [tex]\( x \)[/tex], which represents the number of hours worked by the plumber.
### Step-by-Step Solution
Step 1: Subtract the starting fee from the total bill.
The equation we have is:
[tex]\[ 130 + 56x = 214 \][/tex]
First, we need to eliminate the constant term on the left side ([tex]\(130\)[/tex]). This can be done by subtracting [tex]\(130\)[/tex] from both sides of the equation:
[tex]\[ 130 + 56x - 130 = 214 - 130 \][/tex]
Simplifying both sides:
[tex]\[ 56x = 84 \][/tex]
Step 2: Isolate the variable [tex]\( x \)[/tex] by performing the division property of equality.
Now, we need to solve for [tex]\( x \)[/tex] by dividing both sides of the equation by [tex]\(56\)[/tex]:
[tex]\[ \frac{56x}{56} = \frac{84}{56} \][/tex]
Simplifying:
[tex]\[ x = 1.5 \][/tex]
The remaining steps verify that the division was correct, but you can see that:
[tex]\[ x = 1.5 \][/tex]
### Conclusion
The plumber worked for [tex]\( 1.5 \)[/tex] hours.
Therefore, the number of hours worked by the plumber is 1.5 hours.
