Join the IDNLearn.com community and start finding the answers you need today. Discover comprehensive answers from knowledgeable members of our community, covering a wide range of topics to meet all your informational needs.
Sagot :
Let's solve the given equations one by one and match them to the correct solutions.
1. Equation: 4(3x + 5) - 3 = 9z - 7
- Solution: The x-value that satisfies this equation when expressed in terms of z is [tex]\([\frac{9z}{16} - \frac{7}{2}]\)[/tex]. Notice that this means x is expressed in terms of z. So, there isn't a single numerical value for x, but rather a relationship between x and z.
2. Equation: 5(x + 7) - 3(x - 4) = 7x + 2
- By solving this equation, we find [tex]\( x = 9 \)[/tex].
3. Equation: \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right)
- Solving for z, we get [tex]\( z = 15 \)[/tex].
Given the results we obtained:
- The equation [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex] pairs with [tex]\( \frac{9z}{16} - \frac{7}{2} \)[/tex].
- The equation [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex] pairs with [tex]\( x = 9 \)[/tex].
- The equation [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex] pairs with [tex]\( z = 15 \)[/tex].
Now, let's match this with the given tiles:
- For the equation [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex]:
- This equation does not have a single numerical x-value in the given options since x depends on z. The solution is [tex]\( \frac{9z}{16} - \frac{7}{2} \)[/tex], but this form matches none of the provided x-values exactly.
- For the equation [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex]:
- We have [tex]\( x = 9 \)[/tex]. So, match this to [tex]\( x = 9 \)[/tex].
- For the equation [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex]:
- We have [tex]\( z = 15 \)[/tex]. So, match this to [tex]\( z = 15 \)[/tex].
Valid matches:
- [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex]: [No direct numerical match]
- [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex]: [tex]\( x = 9 \)[/tex]
- [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex]: [tex]\( z = 15 \)[/tex]
Thus:
- [tex]\( \underline{4(3x + 5) - 3 = 9z - 7 \)[/tex] belongs here}
- [tex]\(5(x + 7) - 3(x - 4) = 7x + 2 \longrightarrow x=9\)[/tex]
- [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \longrightarrow z=15\)[/tex]
1. Equation: 4(3x + 5) - 3 = 9z - 7
- Solution: The x-value that satisfies this equation when expressed in terms of z is [tex]\([\frac{9z}{16} - \frac{7}{2}]\)[/tex]. Notice that this means x is expressed in terms of z. So, there isn't a single numerical value for x, but rather a relationship between x and z.
2. Equation: 5(x + 7) - 3(x - 4) = 7x + 2
- By solving this equation, we find [tex]\( x = 9 \)[/tex].
3. Equation: \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right)
- Solving for z, we get [tex]\( z = 15 \)[/tex].
Given the results we obtained:
- The equation [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex] pairs with [tex]\( \frac{9z}{16} - \frac{7}{2} \)[/tex].
- The equation [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex] pairs with [tex]\( x = 9 \)[/tex].
- The equation [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex] pairs with [tex]\( z = 15 \)[/tex].
Now, let's match this with the given tiles:
- For the equation [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex]:
- This equation does not have a single numerical x-value in the given options since x depends on z. The solution is [tex]\( \frac{9z}{16} - \frac{7}{2} \)[/tex], but this form matches none of the provided x-values exactly.
- For the equation [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex]:
- We have [tex]\( x = 9 \)[/tex]. So, match this to [tex]\( x = 9 \)[/tex].
- For the equation [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex]:
- We have [tex]\( z = 15 \)[/tex]. So, match this to [tex]\( z = 15 \)[/tex].
Valid matches:
- [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex]: [No direct numerical match]
- [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex]: [tex]\( x = 9 \)[/tex]
- [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex]: [tex]\( z = 15 \)[/tex]
Thus:
- [tex]\( \underline{4(3x + 5) - 3 = 9z - 7 \)[/tex] belongs here}
- [tex]\(5(x + 7) - 3(x - 4) = 7x + 2 \longrightarrow x=9\)[/tex]
- [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \longrightarrow z=15\)[/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.