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A plumber charges [tex]$\$[/tex]130[tex]$ to start a job plus $[/tex]\[tex]$56$[/tex] per hour. How many hours did she work if the total bill is [tex]$\$[/tex]214$?

This problem can be modeled with this equation:
[tex]\[ 130 + 56x = 214 \][/tex]

Step 1: Which operation should be performed to isolate the variable term?

Apply the subtraction property of equality.

Which value do you need to subtract?
\begin{tabular}{|c|}
\hline
130 \\
\hline
\end{tabular}

[tex]\[ 130 + 56x = 214 \][/tex]

Sagot :

GinnyAnsweridn
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.
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