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.
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To solve the inequality 4/7x - 2/7 > 5/7, let's first isolate the variable x.
Adding 2/7 to both sides of the inequality, we get:
4/7x - 2/7 + 2/7 > 5/7 + 2/7
Simplifying:
4/7x > 7/7
Now, we can simplify the right side:
4/7x > 1
To get x alone, we need to divide both sides by 4/7:
(4/7x)/(4/7) > 1/(4/7)
Simplifying:
x > 7/4
Writing 7/4 as a mixed number:
7/4 = 1 and 3/4
Therefore, the solution to the inequality is x > 1 3/4.