Solve 4/7 x - 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 the variable x on one side.

First, let's simplify the expression on the left side of the inequality:

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

To combine the fractions, we need a common denominator. In this case, the common denominator is 7, so we have:

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

Now we can combine the numerators:

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

We can remove the denominator 7 on both sides of the inequality by multiplying both sides by 7:

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

This simplifies to:

4x - 2 > 5

Next, add 2 to both sides of the inequality to isolate the variable:

4x - 2 + 2 > 5 + 2

4x > 7

Finally, divide both sides of the inequality by 4 to solve for x:

(4x)/4 > 7/4

x > 7/4

The solution to the inequality is:

x > 7/4

In mixed number form, 7/4 can be written as 1 3/4.

Therefore, the solution to the inequality, written with x first and using a mixed number, would be:

x > 1 3/4