To determine which equation represents a proportional relationship, we need to look for relationships where two ratios are equivalent.
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815 = 430: This is a false equation and does not represent a proportional relationship.
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8 over 15 is equal to 4 over 30: Let's check if these ratios are equivalent: \[ \frac{8}{15} = \frac{4}{30} \] Cross-multiplying gives: \[ 8 \times 30 = 240 \quad \text{and} \quad 4 \times 15 = 60 \] Since \(240 \neq 60\), this is not a proportional relationship.
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36 = 63: This is also a false equation and does not represent a proportional relationship.
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3 sixths is equal to 6 thirds: Let's check this one: \[ \frac{3}{6} = \frac{6}{3} \] We simplify both sides: \[ \frac{3}{6} = \frac{1}{2} \quad \text{and} \quad \frac{6}{3} = 2 \] Since \(\frac{1}{2} \neq 2\), this is not a proportional relationship.
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2x12 = 3x18: Let's check if these represent a proportional relationship by simplifying: \[ \frac{2}{3} = \frac{18}{12} \Rightarrow 18 \div 6 = 3 \quad \text{and} \quad 12 \div 6 = 2 \] Cross-multiplying gives: \[ 2 \times 18 = 36 \quad \text{and} \quad 3 \times 12 = 36 \] Since both sides are equal, this does represent a proportional relationship.
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4x18 = x18: This can be simplified by factoring out \(x\): \[ 4x18 = x18 \] Dividing both sides by \(18\) (assuming \(18 \neq 0\)): \[ 4x = x \] This implies an equation but does not provide a direct proportion as one ratio against another for non-zero \(x\).
In summary, the only statement that represents a proportional relationship is:
2x12 = 3x18.