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8\left(3\times 25+3\right)\leq 25\left(3\times 8+1\right)
Multiply both sides of the equation by 200, the least common multiple of 25,8. Since 200 is positive, the inequality direction remains the same.
8\left(75+3\right)\leq 25\left(3\times 8+1\right)
Multiply 3 and 25 to get 75.
8\times 78\leq 25\left(3\times 8+1\right)
Add 75 and 3 to get 78.
624\leq 25\left(3\times 8+1\right)
Multiply 8 and 78 to get 624.
624\leq 25\left(24+1\right)
Multiply 3 and 8 to get 24.
624\leq 25\times 25
Add 24 and 1 to get 25.
624\leq 625
Multiply 25 and 25 to get 625.
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Compare 624 and 625.