Question

one fourth left parenthesis 4 x minus 1 right parenthesis equals negative one fifth minus two fifths

Answer 1

To solve the equation \( \frac{1}{4}(4x - 1) = -\frac{1}{5} - \frac{2}{5} \), we can start by simplifying both sides.

### Step 1: Simplify the right side
Combine the fractions on the right:
\[
-\frac{1}{5} - \frac{2}{5} = -\frac{1 + 2}{5} = -\frac{3}{5}
\]
Now the equation simplifies to:
\[
\frac{1}{4}(4x - 1) = -\frac{3}{5}
\]

### Step 2: Eliminate the fraction on the left side
Multiply both sides by 4 to eliminate the fraction:
\[
4 \cdot \frac{1}{4}(4x - 1) = 4 \cdot -\frac{3}{5}
\]
This simplifies to:
\[
4x - 1 = -\frac{12}{5}
\]

### Step 3: Isolate \( 4x \)
Now, add 1 to both sides. To combine \( 1 \) and \( -\frac{12}{5} \), convert 1 to a fraction with a denominator of 5:
\[
1 = \frac{5}{5}
\]
Thus:
\[
4x - 1 + 1 = -\frac{12}{5} + \frac{5}{5}
\]
This simplifies to:
\[
4x = -\frac{12}{5} + \frac{5}{5} = -\frac{12 - 5}{5} = -\frac{7}{5}
\]

### Step 4: Solve for \( x \)
Now divide both sides by 4:
\[
x = \frac{-\frac{7}{5}}{4} = -\frac{7}{20}
\]

So, the solution to the equation is:
\[
\boxed{-\frac{7}{20}}
\]