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 4/7x - 2/7 > 5/7, we can start by adding 2/7 to both sides:
4/7x - 2/7 + 2/7 > 5/7 + 2/7
4/7x > 7/7
Simplifying both sides of the inequality:
4/7x > 1
Next, we can multiply both sides of the inequality by the reciprocal of 4/7, which is 7/4. As a result, the inequality sign will flip:
(4/7x)(7/4) < (1)(7/4)
(x) < 7/4
To write the rational number 7/4 as a mixed number, we divide the numerator (7) by the denominator (4). The quotient is the whole number part of the mixed number, and the remainder becomes the numerator of the fraction part:
7 ÷ 4 = 1 remainder 3.
Therefore, the solution to the inequality is:
x < 1 3/4 (or x < 1.75)