solve 4/7 x - 2/7 > 5/7. write the rational number in your answer as a mixed number

Answer 1

To solve the inequality 4/7 x - 2/7 > 5/7:

First, we can add 2/7 to both sides of the inequality to isolate the term involving x:

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

Simplifying the equation, we get:

4/7 x > 7/7

Now, we can simplify the right side:

4/7 x > 1

To get x by itself, we will multiply both sides of the inequality by the reciprocal of the coefficient of x, which is 7/4:

(7/4)(4/7) x > 1(7/4)

Simplifying further, we have:

1x > 7/4

Since x is already by itself, we can express the rational number as a mixed number:

x > 1 and 3/4