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Why is [tex]x = 6[/tex] a solution to the proportion [tex]\frac{192}{36} = \frac{32}{x}[/tex]?
A. Because 192 divided by 32 is equal to 6. B. Because 192 divided by 36 is equal to 6. C. Because if you substitute 6 into the equation for [tex]x[/tex] and cross multiply, you get [tex]1,152 = 1,152[/tex]. D. Because if you substitute 6 into the equation for [tex]x[/tex] and cross multiply, you get [tex]1,296 = 1,296[/tex].
2. Cross Multiplication: - To find [tex]\( x \)[/tex], we can cross multiply the terms of the proportion: [tex]\[192 \times x = 36 \times 32\][/tex]
3. Substitution: - Substitute [tex]\( x = 6 \)[/tex] into the equation. [tex]\[192 \times 6 = 36 \times 32\][/tex]
4. Simplifying Both Sides: - Compute the left-hand side: [tex]\[192 \times 6 = 1152\][/tex] - Compute the right-hand side: [tex]\[36 \times 32 = 1152\][/tex]
Therefore, the equation becomes: [tex]\[1152 = 1152\][/tex]
5. Conclusion: - Since both sides of the equation are equal when [tex]\( x = 6 \)[/tex], we can conclude that [tex]\( x = 6 \)[/tex] is indeed a solution to the proportion [tex]\(\frac{192}{36} = \frac{32}{x}\)[/tex].
So the correct statement is: [tex]\[ \text{because if you substitute 6 into the equation for } x \text{ and cross multiply, you get } 1,152 = 1,152.\][/tex]
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