What is the first step in solving for x in the equation 5.6(x+1.42)=7.8 ?

Answer 1

The first step in solving the equation \( 5.6(x + 1.42) = 7.8 \) is to distribute the \( 5.6 \) across the expression \( (x + 1.42) \). This means you will multiply \( 5.6 \) by both \( x \) and \( 1.42 \).

So, you would rewrite the equation as:

\[ 5.6x + 5.6 \cdot 1.42 = 7.8 \]

Calculating \( 5.6 \cdot 1.42 \) gives you a specific value to simplify the equation further. After that, you can proceed to isolate \( x \).

Answer 2

what is the final asnwer

Answer 3

To find the final answer for \( x \) in the equation \( 5.6(x + 1.42) = 7.8 \), let's follow the steps:

1. Distribute \( 5.6 \): \[ 5.6x + 5.6 \cdot 1.42 = 7.8 \] First, calculate \( 5.6 \cdot 1.42 \): \[ 5.6 \cdot 1.42 = 7.952 \] So, the equation becomes: \[ 5.6x + 7.952 = 7.8 \]

2. Isolate \( 5.6x \): \[ 5.6x = 7.8 - 7.952 \] Calculate the right-hand side: \[ 7.8 - 7.952 = -0.152 \] So, the equation is now: \[ 5.6x = -0.152 \]

3. Solve for \( x \): \[ x = \frac{-0.152}{5.6} \] Calculate this value: \[ x = -0.027142857 \approx -0.0271 \quad \text{(rounded to four decimal places)} \]

Therefore, the final answer is: \[ x \approx -0.0271 \]