Let's determine why [tex]\( x = 6 \)[/tex] is a solution to the proportion [tex]\(\frac{192}{36} = \frac{32}{x}\)[/tex].
1. Proportion Analysis:
[tex]\[\frac{192}{36} = \frac{32}{x}\][/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]
