Let's carefully work through solving the equation [tex]\(-\frac{4}{5}(x + 6) = -4x\)[/tex], step by step. Here's how you can solve it:
### Step 1: Eliminate the Fraction
First, let's get rid of the fraction by multiplying both sides of the equation by its reciprocal.
[tex]\[
-\frac{4}{5}(x + 6) = -4x
\][/tex]
To clear the fraction, multiply both sides by [tex]\(-\frac{5}{4}\)[/tex]:
[tex]\[
(x + 6) = 5x
\][/tex]
### Step 2: Simplify the Equation
Next, we simplify the equation by isolating [tex]\(x\)[/tex]:
[tex]\[
x + 6 = 5x
\][/tex]
To isolate [tex]\(x\)[/tex], subtract [tex]\(x\)[/tex] from both sides of the equation:
[tex]\[
6 = 4x
\][/tex]
### Step 3: Solve for [tex]\(x\)[/tex]
Finally, solve for [tex]\(x\)[/tex] by dividing both sides by 4:
[tex]\[
x = \frac{6}{4}
\][/tex]
### Step 4: Simplify the Fraction
Simplify the fraction:
[tex]\[
x = \frac{6}{4} = \frac{3}{2}
\][/tex]
So, the solution to the equation is:
[tex]\[
x = \frac{3}{2}
\][/tex]
Or in decimal form, [tex]\(x = 1.5\)[/tex].
### Summary
By following these steps, we determined that the solution to the equation [tex]\(-\frac{4}{5}(x + 6) = -4x\)[/tex] is [tex]\(x = \frac{3}{2}\)[/tex], which is also equivalent to [tex]\(x = 1.5\)[/tex].
