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.
To solve the inequality, we will isolate x.
First, add 2/7 to both sides of the inequality:
4/7x - 2/7 + 2/7 > 5/7 + 2/7
This simplifies to:
4/7x > 7/7
Next, let's simplify 7/7:
4/7x > 1
To get rid of the fraction, we can multiply both sides by the reciprocal of 4/7, which is 7/4. However, we need to be careful and remember that when we multiply or divide by a negative number, we need to reverse the inequality sign. In this case, the reciprocal is positive, so we don't need to worry about that step:
(4/7x)(7/4) > 1(7/4)
The 4/7 and 7/4 cancel out on the left side, leaving us with:
x > 7/4
To express the answer as a mixed number, divide 7 by 4:
7 ÷ 4 = 1 remainder 3
So the final answer is:
x > 1 3/4