Solve 4/7x−2/7>5/7 . Write the rational number in your answer as a mixed number. Make sure to write your inequality so that x comes first.

Question

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Answer 1

To solve the inequality,

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

First, we need to get rid of the fraction. We can do this by multiplying every term in the inequality by the reciprocal of the denominator, which is 7. This leads to:

7 * (4/7x - 2/7) > 7 * (5/7)

Simplifying this equation gives us:

4x - 2 > 5

Next, we need to isolate x. We can start by adding 2 to both sides of the equation:

4x - 2 + 2 > 5 + 2

Simplifying further, we get:

4x > 7

Finally, we can solve for x by dividing both sides of the equation by 4:

4x/4 > 7/4

Simplifying this gives us:

x > 7/4

In mixed number form, 7/4 can be written as 1 3/4. Therefore, the solution is:

x > 1 3/4