What is the solution to the equation 0.24(x−10.2)=6 when solving for x ?(1 point)

Question

Responses

35.2
35.2

14.8
14.8

16.44
16.44

11.64

Answer 1

To solve the equation \( 0.24(x - 10.2) = 6 \) for \( x \), follow these steps:

1. Distribute 0.24:
   \[ 0.24x - 0.24 \times 10.2 = 6 \] Calculate \( 0.24 \times 10.2 \): \[ 0.24 \times 10.2 = 2.448 \] So we have: \[ 0.24x - 2.448 = 6 \]

2. Isolate the term with \( x \): Add \( 2.448 \) to both sides: \[ 0.24x = 6 + 2.448 \] \[ 0.24x = 8.448 \]

3. Solve for \( x \): Divide both sides by \( 0.24 \): \[ x = \frac{8.448}{0.24} \] Perform the division: \[ x = 35.2 \]

Thus, the solution to the equation is \( \boxed{35.2} \).