Questions: (2x + 4/5)(4x - 8/7) = 0

Transcript text: $\left(2 x+\frac{4}{5}\right)\left(4 x-\frac{8}{7}\right)=0$

Solution

Step 1: Set Up the Equations

The given equation is

\[ (2x + \frac{4}{5})(4x - \frac{8}{7}) = 0 \]

This implies that either

\[ 2x + \frac{4}{5} = 0 \]

\[ 4x - \frac{8}{7} = 0 \]

Step 2: Solve the First Equation

We start with the first equation:

\[ 2x + \frac{4}{5} = 0 \]

To isolate $ x $, we subtract $ \frac{4}{5} $ from both sides:

\[ 2x = -\frac{4}{5} \]

Next, we divide both sides by 2:

\[ x = -\frac{4}{5} \cdot \frac{1}{2} = -\frac{4}{10} = -\frac{2}{5} \]

Step 3: Solve the Second Equation

Now, we solve the second equation:

\[ 4x - \frac{8}{7} = 0 \]

We add $ \frac{8}{7} $ to both sides:

\[ 4x = \frac{8}{7} \]

Next, we divide both sides by 4:

\[ x = \frac{8}{7} \cdot \frac{1}{4} = \frac{8}{28} = \frac{2}{7} \]

Step 4: Summary of Solutions

The solutions to the original equation are:

\[ x = -\frac{2}{5} \quad \text{and} \quad x = \frac{2}{7} \]

The solutions are $ \boxed{x = -\frac{2}{5}} $ and $ \boxed{x = \frac{2}{7}} $.

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