To solve the equation \( 0.4 = -1.1 - \frac{0.8}{x} \), we'll start by isolating the term that contains \( x \).
-
Add \( 1.1 \) to both sides of the equation:
\[ 0.4 + 1.1 = -\frac{0.8}{x} \]
\[ 1.5 = -\frac{0.8}{x} \]
-
Next, to get rid of the negative sign, multiply both sides by -1:
\[ -1.5 = \frac{0.8}{x} \]
-
Now, to eliminate the fraction, multiply both sides by \( x \):
\[ -1.5x = 0.8 \]
-
Finally, divide both sides by -1.5 to solve for \( x \):
\[ x = \frac{0.8}{-1.5} \]
\[ x = -\frac{8}{15} \]
So, the solution is:
\[ x = -\frac{8}{15} \] or approximately \( -0.5333 \).