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.

Answer 1

To solve the inequality, we need to isolate x. First, we will combine like terms on the left side of the inequality:

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

To combine the fractions on the left side, we need to have a common denominator. The common denominator for 7 and 7 is 7. Therefore, we can rewrite the inequality as:

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

Simplifying further:

2/7x > 5/7

Now, to isolate x, we will multiply both sides of the inequality by the reciprocal of 2/7, which is 7/2:

(7/2)(2/7x) > (7/2)(5/7)

Simplifying:

1x > 5/2

This can be written as:

x > 5/2

To express the rational number as a mixed number, we divide the numerator (5) by the denominator (2). The quotient is 2 with a remainder of 1:

x > 2 1/2

Therefore, the solution to the inequality is x > 2 1/2.