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 4/7x - 2/7 > 5/7, you can start by adding 2/7 to both sides of the inequality to isolate the term with x:

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

Simplifying the equation gives:

4/7x > 7/7

The right side of the inequality can be simplified further:

4/7x > 1

Now to solve for x, you need to multiply both sides of the inequality by the reciprocal of 4/7, which is 7/4:

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

This simplifies to:

(4*7)/(7*4)x > 7/4

28/28x > 7/4

Simplifying both sides of the inequality gives:

x > 7/4

To write the rational number 7/4 as a mixed number, you divide the numerator (7) by the denominator (4). The quotient is the whole number, and the remainder is the numerator of the fraction part:

7 ÷ 4 = 1 remainder 3

So the mixed number form of 7/4 is 1 3/4.

Therefore, the solution to the inequality 4/7x - 2/7 > 5/7, written as a mixed number, is:

x > 1 3/4