Question

a plumber charges $130 to start a job plus $56 per hour. how many hours did she work if the total bill is $214? this problem can be modeled with this equation: 130 + 56x = 214. 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? 130 step 2: which operation should be performed to make the coefficient of x equal to 1? apply the dropdown property of equality. dropdown options: addition, subtraction, division check right side image: 130+56x = 214 -130 -130 +56x = 84

Explanation:

Step1: Analyze the equation after Step 1

After subtracting 130 from both sides, we have \(56x = 84\). To make the coefficient of \(x\) equal to 1, we need to perform an operation that will isolate \(x\). Since \(x\) is multiplied by 56, we use the inverse operation of multiplication, which is division.

Step2: Determine the operation

The equation is \(56x = 84\). To solve for \(x\), we divide both sides of the equation by 56. This is applying the division property of equality, which states that if \(a = b\), then \(\frac{a}{c}=\frac{b}{c}\) (where \(c
eq0\)). So we divide both sides by 56: \(\frac{56x}{56}=\frac{84}{56}\), which simplifies to \(x = \frac{84}{56}=1.5\). But for the question about the operation to make the coefficient of \(x\) equal to 1, the operation is division.

Answer:

division