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: \[ \boxed{-\frac{7}{20}} \]