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Try It: Solving a Word Problem Using an Equation

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

This problem can be modeled with the equation:

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

Step 1: Which operation should be performed to isolate the variable term?
Apply the [tex]\(\square\)[/tex] property of equality.

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Answer :

GinnyAnswer
To solve the equation [tex]\(130 + 56x = 214\)[/tex], we need to isolate the variable [tex]\(x\)[/tex]. Follow these steps:

### Step 1: Isolate the Variable Term
First, we need to eliminate the constant term (130) from the left side of the equation. To do this, we perform the following operation:

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

So, we subtract 130 from both sides of the equation:

[tex]\[ 56x = 84 \][/tex]

### Step 2: Solve for [tex]\(x\)[/tex]
Next, we need to isolate [tex]\(x\)[/tex] by getting rid of the coefficient 56. To do this, we divide both sides of the equation by 56:

[tex]\[ x = \frac{84}{56} \][/tex]

### Step 3: Simplify the Fraction
Finally, we simplify the fraction:

[tex]\[ x = 1.5 \][/tex]

### Conclusion
The plumber worked for 1.5 hours.

Therefore, the plumber worked for [tex]\(1.5\)[/tex] hours to result in a total bill of \$214.

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