What is the sum of the solutions to (x − 6)(x + 0.7) = 0 ?

Options

A. `−6.7`
B. `−5.3`
C. 5.3
D. 6.7

Explanation

To solve the equation \((x - 6)(x + 0.7) = 0\) and find the sum of its solutions, we can follow these steps:

### Step 1: Set each factor to zero
The equation is in factored form, which means we can find the solutions by setting each factor equal to zero.

\[ x - 6 = 0 \quad \text{and} \quad x + 0.7 = 0 \]

### Step 2: Solve for \(x\) in each equation
1. For the first equation \(x - 6 = 0\):
\[ x = 6 \]

2. For the second equation \(x + 0.7 = 0\):
\[ x = -0.7 \]

### Step 3: List the solutions
The solutions to the equation are:
\[ x_1 = 6 \quad \text{and} \quad x_2 = -0.7 \]

### Step 4: Calculate the sum of the solutions
To find the sum of the solutions, we add \(x_1\) and \(x_2\):
\[ \text{Sum} = x_1 + x_2 = 6 + (-0.7) = 6 - 0.7 = 5.3 \]

### Final Answer
The sum of the solutions is:
\[ \boxed{5.3} \]

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