To isolate the variable term [tex]\(x\)[/tex] in the equation [tex]\(130 + 56x = 214\)[/tex], we need to perform the following steps:
### Step 1: Subtract 130 from both sides
We need to eliminate the constant term on the left side, which is 130. To do this, we subtract 130 from both sides of the equation.
[tex]\[130 + 56x - 130 = 214 - 130\][/tex]
### Step 2: Simplify both sides
Simplifying both sides will give us:
[tex]\[56x = 84\][/tex]
### Step 3: Divide both sides by 56
To solve for [tex]\(x\)[/tex], we now 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]
### Step 4: Simplify the right side
Simplifying the right side will give us:
[tex]\[x = 1.5\][/tex]
### Conclusion
Thus, the plumber worked for 1.5 hours to achieve a total bill of $214.
