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

Question

0.24
(
𝑥
−
10.2
)
=
6
when solving for x
𝑥
?(1 point)
Responses

35.2
35.2

14.8
14.8

11.64
11.64

16.44..

Answer 1

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

1. Distribute the \(0.24\) 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 to isolate the term with \(x\): \[ 0.24x = 6 + 2.448 \] Calculate \(6 + 2.448\): \[ 6 + 2.448 = 8.448 \] Now the equation is: \[ 0.24x = 8.448 \]

3. Divide both sides by \(0.24\) to solve for \(x\): \[ x = \frac{8.448}{0.24} \] Now perform the division: \[ x = 35.2 \]

Thus, the solution for \(x\) is \(35.2\).