4/7x-2/7>5/7

1 answer

To solve the inequality \( \frac{4}{7}x - \frac{2}{7} > \frac{5}{7} \), follow these steps:

  1. Get rid of the fractions by multiplying all terms by 7 (which is a positive number, so the direction of the inequality does not change):

    \[ 7 \left( \frac{4}{7}x \right) - 7 \left( \frac{2}{7} \right) > 7 \left( \frac{5}{7} \right) \]

    This simplifies to:

    \[ 4x - 2 > 5 \]

  2. Add 2 to both sides of the inequality:

    \[ 4x - 2 + 2 > 5 + 2 \]

    This simplifies to:

    \[ 4x > 7 \]

  3. Divide by 4:

    \[ x > \frac{7}{4} \]

So the solution to the inequality is:

\[ x > \frac{7}{4} \]

Or in decimal form:

\[ x > 1.75 \]