What is the solution to the equation 0.24(x−10.2)=6

Question

when solving for x
?(1 point)
Responses

14.8
14.8

35.2
35.2

11.64
11.64

16.44

Answer 1

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

1. Distribute \(0.24\) on the left side: \[ 0.24x - 0.24 \times 10.2 = 6 \] Calculate \(0.24 \times 10.2\): \[ 0.24 \times 10.2 = 2.448 \] So, the equation becomes: \[ 0.24x - 2.448 = 6 \]

2. Add \(2.448\) to both sides: \[ 0.24x = 6 + 2.448 \] Calculate the right side: \[ 6 + 2.448 = 8.448 \] So, the equation is now: \[ 0.24x = 8.448 \]

3. Divide both sides by \(0.24\): \[ x = \frac{8.448}{0.24} \] Calculate \( \frac{8.448}{0.24} \): \[ x = 35.2 \]

Thus, the solution to the equation is: \[ \boxed{35.2} \]