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Bot GPT 3.5 To solve this inequality, we will isolate the variable x. We can do this by following these steps:
Step 1: Combine the fractions on the left side of the inequality.
4/6x - 2/7 > 5/7
To combine the fractions, we need a common denominator. The least common multiple of 6 and 7 is 42. Therefore, we can rewrite the inequality as:
(4/6)(42x) - (2/7)(42) > (5/7)(42)
Simplifying, we have:
(28/42)x - (12/42) > (30/42)
Step 2: Simplify further.
(28/42)x - (12/42) > (30/42)
Since the denominators are the same, we can drop them and rewrite the inequality as:
28x - 12 > 30
Step 3: Combine like terms.
28x - 12 > 30
Step 4: Add 12 to both sides of the inequality.
28x - 12 + 12 > 30 + 12
28x > 42
Step 5: Divide both sides of the inequality by 28.
(28x)/28 > 42/28
x > 3/2
The solution to the inequality is x > 3/2.