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.
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(1 point)
To solve the inequality 4/7x - 2/7 > 5/7, we need to isolate the variable x.
First, let's add 2/7 to both sides of the inequality:
4/7x - 2/7 + 2/7 > 5/7 + 2/7
Simplifying, we get:
4/7x > 7/7
Next, let's multiply both sides of the inequality by the reciprocal of 4/7, which is 7/4:
(7/4)(4/7x) > (7/4)(7/7)
Simplifying, we get:
x > 7/4
To write the rational number 7/4 as a mixed number, we divide 7 by 4:
7 ÷ 4 = 1 remainder 3
So, the mixed number representation of 7/4 is 1 3/4.
Therefore, the solution to the inequality is x > 1 3/4.